The Blues hitman attracted strong interest from the Chinese Super League in January.
And the 28-year-old also pushed for a return to Atletico Madrid before the start of the season.
Chelsea have been keen to tie Costa down long-term with his value obvious to Antonio Conte’s team.
Diego Costa's left the door open to leaving Chelsea despite a league title being on the cards
However, his future remains somewhat in limbo, with Chelsea preparing for life without him.
A move for Everton hitman and former Blues forward Romelu Lukaku is being lined up, while Real Madrid’s Alvaro Morata is also on Conte’s radar.
Costa does not insist he will leave, but even on the back of a successful first season under Conte, it may not be enough to keep the Spain international in west London.
Antonio Conte wants Diego Costa to stay at Chelsea ahead of a return to the Champions League
Was this challenge on Diego Costa a penalty?
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Chelsea striker Diego Costa could yet return to Atletico Madrid
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