Having missed out on signing Romelu Lukaku to Manchester United, it may well be best to try and keep hold of Costa, but ESPN report that he has little interest remaining in SW6 next season.
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.
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.
Costa has scored 52 goals in EPL action since joining the Pensioners in 2014, and has made it no secret that he wishes to play anywhere, except for China, and that he'd prefer Atletico Madrid.
Other options are also coming into the play as the Spanish outlet could let the striker go at a Chinese club for sixth months loan, where he can continue playing.
Alvaro Morata is Conte's next preferred choice to replace Costa if Lukaku can not be prevented from joining United, and there is mutual respect between the two men that stretches back to the summer of 2014, when Conte pushed for Juventus to sign him from Real Madrid.