The Russian spent last season on loan at Villareal and impressed, scoring six goals and registering nine assists in all competitions for the club.
However, he is thought to be keen on playing regular football at the Bernabeu but is unlikely to get it, with the likes of Cristiano Ronaldo, Gareth Bale, James Rodriguez and Isco all ahead of him in the pecking order.
That has sparked talk of a permanent move away from Spain, with both Everton and Liverpool said to be interested, with the Blues in particular mentioned as having kept an interest in him from two years ago.
There are however, several complications to any potential deal. The first would be price, with AS claiming that a bid of around £10-14million would be needed to tempt Madrid into a sale, which is surely out of Everton's price range.
Second is new boss Rafa Benitez, who is thought to be keen to use what's available to him rather than signing more stars, and Cheryshev would be among them. It is also thought that he would only allow him to leave should a suitable replacement be found, again scuppering a deal.
If it were to happen though, there's no denying he would be an improvement, and coupled with the signing of Gerard Deulofeu, Everton would have serious talent on the wings for next season.