user1816: In the current World Championship cycle Magnus Carlsen has a psychological edge on Nepo. While Carlsen already knows who he is going to face in the WC match, Nepo has to wait for him to announce his intention to defend his title before knowing who his opponent is.
The longer Magnus delays the announcement, the more serious this asymmetrical situation becomes in terms of preparation and planning.
Has Magnus been given a deadline by which time he must announce his intentions?

user-1: We'll probably have to wait much longer (sigh)
According to chess24,

It's still unclear when the chess world will get closer to an answer
as to who will play the next World Championship match. Sutovsky said
during the Candidates that Carlsen was given an "informal deadline" of
around July 20, hinting a decision could come around that time.
Speaking to Aftenposten today, FIDE's General Director walked back his
statements, calling it a misunderstanding and saying that a deadline
or ultimatum was never given. "It's definitely not like Magnus has to
make a decision before July 20", he added.
"FIDE is not pushing for Magnus to make a decision. We would rather
continue to discuss and wait if necessary, as long as it leads to him
playing. There is no date set for Magnus to make a decision."
"When the contract has been made and sent, the normal procedure is
that a deadline is indicated there. There is no contract at the
moment, that has to come first," Sutovsky says.

Of relevance is also this tweet by Tarjei J. Svensen, the author of the above-cited article. It reads

FIDE supposedly asked Carlsen to make a decision before July 20. It would be extraordinary if he makes it 9-10 months before it's scheduled to take place, and before receiving contracts. In the past the final decision was made only when signed, a few months before.

Update
Magnus Carlsen Will Not Defend World Championship Title

user32821: Well, he has been 'asked':
https://www.theguardian.com/sport/2022/jul/08/magnus-carlsen-given-world-chess-title-deadline-ian-nepomniachtchi-ding-liren-await
But, in my opinion, if he doesn't play, then it will be against the spirit of game. He's reigning champion but choosing whether to play or not against particular player is purely nonsense.
'A player cannot run away from their duties'
'A winner never leaves, and a leaver never wins'
And if he gets away, FIDE should take some action against him.

user-1: UPDATE: Magnus Carlsen announced on July 20th that he wouldn't defend his title in the 2023 championship.
He said he didn't feel enough motivation and wouldn't gain much from it. He said, verbatim, "I simply won't play the match." He didn't rule out the possibility to participate in such matches in the future but added you should not particularly count on it. However, he is going to continue playing FIDE events and doesn't plan to end his career any time soon. He still thinks of reaching 2900 Elo.
You can watch his interview on YouTube to get more details:
kunal chess (channel), video: It’s official! Magnus Carlsen will NOT defend his title, time stamp: 51:03. Before that moment they mainly discuss poker and Magnus's experience in Las Vegas.
OLD ANSWER (July, 9)
I don't think there's a very strict deadline set for Magnus but the director general of FIDE said that there should be some information in about a couple of weeks, around July 20th or so. That's what they expect of him. FIDE can't wait ad infinitum. They have to plan a lot of things ahead. It's probably preliminary information. The director general talked to Magnus and they seemed to have a more or less constructive conversation about Magnus's wishes, which was private, I guess. However, you can find the director general on YouTube. He discusses this issue during chesscom broadcast of the 2022 FIDE Candidates with Robert Hess.
I don't see many uploads with FIDE Director General (Emil Sutosvky) discussing it with Robert Hess. However, chesscom original broadcast of 2022 FIDE Candidates is still available as of now (July 2022). It's round 14, time stamp 1:32 on YouTube.
Note. I've decided to make this answer Community Wiki. I think it's in line with questions and answers of that sort.

1816: <p>In the current World Championship cycle Magnus Carlsen has a psychological edge on Nepo. While Carlsen already knows who he is going to face in the WC match, Nepo has to wait for him to announce his intention to defend his title before knowing who his opponent is.</p>
<p>The longer Magnus delays the announcement, the more serious this asymmetrical situation becomes in terms of preparation and planning.</p>
<p>Has Magnus been given a deadline by which time he must announce his intentions?</p>
 -1: <h2>We'll probably have to wait much longer (sigh)</h2>
<p><a href="https://new.chess24.com/wall/news/sources-zero-chance-carlsen-plays-title-match-unless-drastic-format-changes" rel="nofollow noreferrer">According to chess24</a>,</p>
<blockquote>
<p>It's still unclear when the chess world will get closer to an answer
as to who will play the next World Championship match. Sutovsky said
during the Candidates that Carlsen was given an &quot;informal deadline&quot; of
around July 20, hinting a decision could come around that time.</p>
<p><a href="https://www.aftenposten.no/sport/sjakk/i/dn65Bz/sjakktoppens-carlsen-uttalelse-skapte-internasjonale-overskrifter-naa-mener-han-seg-misforstaatt" rel="nofollow noreferrer">Speaking to Aftenposten today</a>, FIDE's General Director walked back his
statements, calling it a misunderstanding and saying that a deadline
or ultimatum was never given. &quot;It's definitely not like Magnus has to
make a decision before July 20&quot;, he added.</p>
<p>&quot;FIDE is not pushing for Magnus to make a decision. We would rather
continue to discuss and wait if necessary, as long as it leads to him
playing. There is no date set for Magnus to make a decision.&quot;</p>
<p>&quot;When the contract has been made and sent, the normal procedure is
that a deadline is indicated there. There is no contract at the
moment, that has to come first,&quot; Sutovsky says.</p>
</blockquote>
<p>Of relevance is also <a href="https://twitter.com/TarjeiJS/status/1544340217100136448?s=20&amp;t=R_MPKZ-QjYzGkcVBQYL9dg" rel="nofollow noreferrer">this</a> tweet by Tarjei J. Svensen, the author of the above-cited article. It reads</p>
<blockquote>
<p>FIDE supposedly asked Carlsen to make a decision before July 20. It would be extraordinary if he makes it 9-10 months before it's scheduled to take place, and before receiving contracts. In the past the final decision was made only when signed, a few months before.</p>
</blockquote>
<h2>Update</h2>
<p><a href="https://www.chess.com/news/view/magnus-carlsen-not-to-defend-chess-world-title" rel="nofollow noreferrer">Magnus Carlsen Will Not Defend World Championship Title</a></p>
 32821: <p>Well, he has been 'asked':
<a href="https://www.theguardian.com/sport/2022/jul/08/magnus-carlsen-given-world-chess-title-deadline-ian-nepomniachtchi-ding-liren-await" rel="nofollow noreferrer">https://www.theguardian.com/sport/2022/jul/08/magnus-carlsen-given-world-chess-title-deadline-ian-nepomniachtchi-ding-liren-await</a></p>
<p>But, in my opinion, if he doesn't play, then it will be against the spirit of game. He's reigning champion but choosing whether to play or not against particular player is purely nonsense.
'A player cannot run away from their duties'
'A winner never leaves, and a leaver never wins'
And if he gets away, FIDE should take some action against him.</p>
 -1: <p><strong>UPDATE: Magnus Carlsen announced on July 20th that he wouldn't defend his title in the 2023 championship.</strong></p>
<p>He said he didn't feel enough motivation and wouldn't gain much from it. He said, verbatim, &quot;I simply won't play the match.&quot; He didn't rule out the possibility to participate in such matches in the future but added you should not particularly count on it. However, he is going to continue playing FIDE events and doesn't plan to end his career any time soon. He still thinks of reaching 2900 Elo.
You can watch his interview on YouTube to get more details:
kunal chess (channel), video: <em>It’s official! Magnus Carlsen will NOT defend his title</em>, time stamp: 51:03. Before that moment they mainly discuss poker and Magnus's experience in Las Vegas.</p>
<p><strong>OLD ANSWER (July, 9)</strong>
I don't think there's a very strict deadline set for Magnus but the director general of FIDE said that there should be some information in about a couple of weeks, around July 20th or so. That's what they expect of him. FIDE can't wait ad infinitum. They have to plan a lot of things ahead. It's probably preliminary information. The director general talked to Magnus and they seemed to have a more or less constructive conversation about Magnus's wishes, which was private, I guess. However, you can find the director general on YouTube. He discusses this issue during chesscom broadcast of the 2022 FIDE Candidates with Robert Hess.</p>
<p>I don't see many uploads with FIDE Director General (Emil Sutosvky) discussing it with Robert Hess. However, chesscom original broadcast of 2022 FIDE Candidates is still available as of now (July 2022). It's round 14, time stamp 1:32 on YouTube.</p>
<p>Note. I've decided to make this answer Community Wiki. I think it's in line with questions and answers of that sort.</p>
