The Spaniard, 28, has been linked with a move having been told he is not part of manager Antonio Conte's plans.
Costa did not train on Monday, with both parties understood to be keen to avoid unnecessary distractions.
"It was agreed with the club that he should have an extra few days off," said a statement on the club's website.
Costa is expected to stay away for at least the remainder of this week.
The striker was the only player missing from Chelsea's Cobham training ground other than Antonio Rudiger, who only joined the club on Sunday.
Costa revealed to reporters last month that Conte had told him via text message he was not under consideration for selection, and Conte's view is said to have not changed.
Sources have told BBC a deal for the Spain international to leave the club could go through in the coming weeks.
Costa scored 20 goals in 35 Premier League games last season to help the Blues win the Premier League title.
He has been linked with a return to Atletico Madrid, despite the Spanish club being banned from signing players until the January transfer window.
Brazil-born Costa spent four seasons with Atletico before joining Chelsea for a reported £32m in 2014.
In January, Costa was left out of the Chelsea side for an away match at Leicester after he was involved in a dispute with a fitness coach.
It followed reports of an offer from China that would have been worth £30m a year in salary. At the time, Chelsea said they had no intention of selling him.
Striker Diego Costa has been given extra time off by Chelsea, increasing the likelihood of him leaving during the summer transfer window.