The Reds are reportedly looking at potential replacements for Raheem Sterling, and the Russian fits the bill.
The Reds could offer between €15-20million for the midfielder, which would work out at between £10-14million for the 24-year-old.
The Russia international spent last year on loan at Villareal, where he impressed, scoring seven goals and registering eight assists in 26 La Liga games. It is believed that Brendan Rodgers' side view him as a perfect replacement for want-away star Raheem Sterling, with his versatility in a number of positions a big selling point.
They are also likely to persuade the player into a move to England with the promise of firs- team football, given he is unlikely to be guaranteed playing time ahead of the likes of Cristiano Ronaldo, Gareth Bale, Isco and James Rodriguez at the Bernabeu.
However, there could be one thing that will scupper the deal, and that is former manager Rafa Benitez. The Spaniard was recently confirmed as Carlo Ancelotti’s replacement and according to Cadena Ser, is keen to work with the players he currently has rather than recruit further, including loaned out players Cheryshev and Casemiro.
If the Russian were to decide he wants to leave the Spanish capital, it is unknown whether the La Liga giants would want to include a buy-back clause, similar to the deal they struck with Juventus for Alvaro Morata.