Starsport understands the AWOL Spain striker now accepts he does not have a legal case against the champions, whose manager Antonio Conte axed him by text this summer.
Costa is climbing down in a bid to resurrect his career after failing to secure a move back to his former club Atletico Madrid on Friday.
The two clubs were unable to agree a deal, with the Spanish side still operating under a transfer ban until January.
Costa, 28, has been holed up in his hometown of Lagarto in Brazil for the last two months with Chelsea fining him for failing to report back for training.
But having accused the club of treating him like a criminal he now appears to have accepted he has no alternative but to return to the Blues, who he helped land the title last season with 20 league goals.
A source close to Costa said last night: “I guess there will have to be a reconciliation between Diego and the club.
“I think he will have to come back because he does not want his career to end there, like this.
“Diego has no grounds to sue Chelsea. Chelsea do have grounds to sue Diego now.”
It is understood Costa’s legal advisers looked into whether they could argue Chelsea were guilty of constructive dismissal, thereby entitling him to terminate his contract and leave the Blues.
But legal experts say such a claim was “tenuous” and it appears he has now abandoned the idea.
The Blues are still looking into suing Costa for breach of contract.
It is understood with the World Cup in Russia next summer, Costa knows he cannot afford to remain in limbo until the new year and by rejoining Chelsea he can at least get fit while avoiding further potential legal issues.
Conte though looks certain to snub Costa if he turns up again and it is likely he will be told to train with the club’s Under-23s with little or no prospect of a return to the first team.
