The 28-year-old is currently believed to be in his native Brazil, having failed to return from his summer break after Blues boss Antonio Conte decided to exclude him from his first-team plans this season.
Costa's representatives have thus far failed to secure him a move to a new club, with his preferred destination of Atletico Madrid unable to sign new players until January.
Chelsea are said to be planning to fine the Spain international around £300,000 for allegedly failing to report back for training, albeit with the Blues' youth setup, while they are also thought to have concerns that he has put on weight during his extended summer break.
Meanwhile, an aggrieved Costa is rumoured to be plotting legal action against Chelsea for being ousted from the first team and, according to The Mirror, part of his claim is for an unpaid 'loyalty' bonus.
The demand comes despite the striker currently being AWOL and despite admitting numerous times last season that he would prefer to move to another club.
Costa last featured for Chelsea in May, scoring his side's only goal as they lost the FA Cup final to Arsenal at Wembley.