Costa has been linked with a return to Atleti in recent weeks. He has been yearning for a move to his previous club Atletico Madrid.
The Blues' top scorer will be unable to play until January as Atletico are now under a transfer embargo.
So far this transfer window, the Blues have already lost out to Manchester United in the race to sign Belgium striker Romelu Lukaku from Everton, even though Chelsea matched Manchester Utd's £75 million bid.
And yesterday Chelsea confirmed the signing of Monaco powerhouse Tiemoue Bakayoko. However, it is likely that the Belgian youngster will again be used as backup and a more household name will be brought to Stamford Bridge.
Newcastle United 'preparing £10m Sheyi Ojo bid'
Ojo was part of the World Cup winning England U20 squad this summer and is highly-rated by many behind the scenes at Liverpool . Ojo and Murphy have both appeared on Newcastle's wishlist, with Rafael Benitez determined to strengthen his options out wide.
Samajwadi Party stands divided on eve of Presidential polls
While the SP has backed Opposition's nominee Meira Kumar's candidature, Shivpal's announcement is a new twist in the tale. Meanwhile, Mulayam's brother and SP MLA Shivpal Singh Yadav announced his support for Kovind in Varanasi last week.