According to Spanish newspaper AS, Turan's agent Ahmet Bulut has informed Atletico that he's in discussions with United and Chelsea having informed the Spanish club that his player is seeking a new challenge.
Barcelona have recently been linked with the Turkish international too, but it's believed that Turan wants to leave Spain with the Premier League his preferred destination.
Jorge Mendes is also involved in the deal, so it's no surprise that Chelsea and Manchester United are the two frontrunners.
Chelsea have raided Atletico Madrid before, signing Diego Costa and Filipe Luis last summer. Goalkeeper Thibaut Courtois also spent three highly successful years on loan there so the two clubs are well acquainted.
Manchester United meanwhile have also been long term admirers of the midfielder, and Spanish reports earlier this week had claimed that Louis van Gaal was ready to offer around €39m for Turan.
That's just off his release clause which is thought to be €41m.
As for Turan, AS reports that he would be happy to join either Chelsea or United so it may ultimately come down to which club is preferred to stump up the most money for him.
What do you think - will Turan end up at Chelsea, Manchester United, Atletico Madrid or somewhere else entirely come the end of transfer window?