Meanwhile, Manchester United have reportedly sealed a deal to bring Everton's Romelu Lukaku to Old Trafford, ending speculation the Belgian would re-sign for the Blues.
The Premier League champions have no plans to allow Costa extended leave from training until an agreement is reached for his sale, despite the fact that his relationship with Conte appears damaged beyond fix and he has reportedly begun to say goodbye to his Chelsea teammates.
"With Atletico set to make their opening bid to re-sign Costa, the Spain worldwide has got in touch with a number of his Chelsea team-mates to tell them he expects to return to his former club and is unsure whether he will be back at Chelsea for pre-season training which starts next Monday".
The loss of Costa only compounds the problem at the feet of Antonio Conte, who told the striker he did not want him at the club.
Indeed, the same story reveals that Costa won't be allowed to skip Chelsea's pre-season campaign if the Blues haven't agreed a transfer deal with Atletico.
"His decision to tell Costa that he is no longer part of his plans by text message looks increasingly ill-advised and has complicated Chelsea's transfer plans". Costa scored 27 goals in all competitions last season under Conte, cementing himself as one of the best strikers in the Premier League for another season.