Diego Costa, 28, scored 20 goals to help Chelsea lift the Premier League title.
But his season was soured by events in January when he had a bust up with Conte on the training ground and was dropped for the next match.
The fallout came in the wake of interest from China – when a move would have seen made one of the highest earning players in the world.
And his future remained in doubt despite the decision to stay put until the end of the season.
Interest from Chinese Super League side Tianjin Quanjian has remained while former club Atletico Madrid were keen on a deal before having their transfer ban upheld.
The Spain international has since ruled out a move to China, which has increased the tension between him and Conte, and he insisted he would only consider a return to former club Atletico.
But a transfer back to Spain has been put in doubt with Atletico banned from signing new players until January.
Chelsea are closing in on a deal to sign Romelu Lukaku back from Everton and have also been linked with Alvaro Morata.
And Conte appears to be keen to move Costa on to help fund his summer spree.
Costa claims Conte sent him a message telling him he was not part of his plans and admits he will now have to find a new club – with a World Cup to be ready for at the end of next season.
Speaking after Spain’s 2-2 draw in Colombia, Costa said: “Antonio Conte has told me by message that I will not continue with Chelsea and that’s it.
“My relationship with the coach has been bad this season and it is clear that he does not want me on the team.
“I guess I have had such a bad season that I can’t continue.
“Right now I’m a Chelsea player because I have a contract, but the coach does not want me there. I have to find a new team.”
When asked whether a return to Atletico is next on the cards for him, he added: “Five months without playing? I do not know, it’s complicated.
“But people know that I love Atletico a lot and that I love living in Madrid.
“It would be nice to go back, but it’s difficult to go four or five months without playing and it’s a World Cup year.
“There’s a lot to think about. I need to play, that’s all.”
Costa is contracted to Chelsea until the summer of 2019 but a move away this summer now looks certain.