The Sun says he faces a fine up to £300k after going AWOL.
The Spanish striker, 28, was due to report for training at the Premier League champions TWO WEEKS ago.
But he has been pictured partying in Brazil instead of returning to the club's Cobham HQ and working on his fitness.
Antonio Conte has made it clear Costa is not part of his plans and would be training away from the first team.
But Costa was still due to return and keep himself in shape for a potential move.
He now could be fined by the club two weeks wages with his current earnings £150,000 a week.