The Spain international was left out of the Blues’ Community Shield squad to face Arsenal despite Mourinho insisting before the game he would be fit to play.
The Blues boss has now admitted the striker could miss the visit of Swansea on Saturday as the champions kick off their title defence at Stamford Bridge.
“I don’t know if Diego Costa will be available for the start of the season," he told BT Sport.
“He had a little problem after the Barcelona game. After that he was training normally and we thought he would be ready, but this morning he was feeling uncomfortable."
Costa finished last season as Chelsea's top scorer with 20 Premier League goals but was forced to miss the end of the season due to problems with his hamstring.
