That’s according to Turkish news outlet Milliyet who reckon a deal is on the cards.
It’s suggested the maverick forward will arrive in Istanbul later today ahead of a prospective move.
The Spain international will complete a medical and - assuming it’s successful - he’ll compete a loan move to the Super Lig heavyweights.
The move won’t be particularly beneficial to Chelsea, though.
Milliyet say the Blues will cough up a whopping 75 per cent of his salary.
The Turkish transfer window is open until Friday meaning Costa can still leave the west Londoners.
Antonio Conte told Costa he is surplus to requirements at Stamford Bridge earlier this summer - and the Brazil-born forward has been AWOL in his homeland since.
The Spain international is keen on a return to Atletico having left the club in 2014.
But the La Liga giants are banned from making any signings until January due to a transfer embargo.
He was dumped via text message by Blues boss Conte.
Conte wrote: "Hi Diego, I hope you are well. Thanks for the seasono [sic] we spent together."
Costa has bagged 52 goals in 89 games for Chelsea since joining the club in 2014.
