While eager to get Costa back on board, the Atletico supremo has moved to rubbish any suggestion that Diego Simeone's decision to commit to fresh terms is linked to a deal for the Spain global. He has been trying to push through a transfer to his former club Atletico Madrid, but did not succeed.
The Spain international's preferred move to Atletico was not possible over the summer due to the La Liga side's transfer ban, while various stop-gap loan possibilities to the likes of AC Milan, Las Palmas and Fenerbahce all proved fruitless.
However, the Turkish window has now since closed, forcing the striker to officially stay at Chelsea until at least January.
As The Sun report, Costa was included by the Blues for their Premier League squad, but is yet to return to England in order to return to training at Cobham.
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Costa has already been out of action for the first month of this season, with Stamford Bridge manager Antonio Conte no longer considering him in his plans for the campaign ahead.
Meanwhile the Sunday Express claim that Atletico Madrid have sent officials to London to talk through the details of his likely transfer to the Wanda Metropolitano stadium in January.
But Costa has said he wants to join Atletico Madrid, who cannot sign him until January because of a transfer ban.