The Spanish club are hoping to rush through a deal before Costa's scheduled return to pre-season training with Chelsea next week.
And despite winning the title with the Blues last term, Costa angered Antonio Conte by trying to force a move away from Stamford Bridge in January. I have no preference for a league, I just want to play'. Owing to the transfer ban now imposed on Atletico Madrid, it was believed that they will not sign the 28-year-old anytime soon, as was the case with their pursuit of Alexandre Lacazette - which ended in disappointment as their transfer ban was not upheld.
The disappointment on missing out on Lacazette means Atletico are now likely to focus on buying back Costa.
Even if they sign Costa this summer, he can not play for them until January because they can not register players due to a Federation Internationale de Football Association ban.
Chelsea remain adamant they will not be forced into accepting a deal with which they are displeased however with Costa only demanding a reunion with Atletico, they might be unable to command a high price for their leading scorer last season.
Costa initially left Atletico for Chelsea for a fee of around £32m in the summer of 2014, though he has never really settled in London.