Costa is yet to return to the club this summer and remains in Brazil after being told he is not wanted by Antonio Conte.
He is unlikely to ever play for the club again but has been included in their Premier League squad following the close of the transfer window.
Costa was informed by text that he was no longer wanted and was keen to complete a move back to Atletico Madrid before the Spanish deadline closed tonight.
Express Sport understands Chelsea were asking for £50m to sign off on the deal.
But their step to include him in their squad comes as a surprise despite the transfer now looking unlikely.
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Even if Costa does manage to sign for Atletico before the window shuts he can’t play until January due to their transfer embargo.
A loan move has been mooted but time is running out. Costa has claimed he has been treated like a criminal to which Conte laughed hysterically at his press conference.
Chelsea signed Alvaro Morata to replace Costa but failed to land Fernando Llorente on deadline day after he moved to Tottenham instead.