The versatile player says he has spoken to new boss Brendan Rodgers but admits there is, as yet, nothing to sign as his current contract draws to an end.
"I'm happy," he said. "I want to stay, but the longer it goes on, you start to wonder if it's going to happen.
"I've spoken to the manager and he wants me to stay, which is important for me. You want to feel wanted."
The 30-year-old, who can play in defence and midfield, started his second spell with Celtic after leaving Aberdeen in 2010
"Hopefully we can come to some kind of agreement soon," said Mulgrew, who only made 20 appearances last season in an injury-disrupted season.
"There's no offer on the table yet, but I think it's moving towards that this week."
Mulgrew says he wants to be part of what he believes will be a time of progress at the club under Rodgers.
"The new manager's plans for the club are great," he said after coming on as a substitute in Scotland's 3-0 defeat by France on Saturday.
"It's exciting times ahead for Celtic. I hope I can be involved in that because I think there's a few big years coming up.
"It's not as quick as just signing it. These things are never quick.
"There's bits and pieces that need tied up, things need done, but hopefully we can get it done as quickly as possible."
Charlie Mulgrew admits his future is still up in the air as he continues to wait to be offered a new Celtic deal.