Cheryshev could be a useful player for Rafa Benítez next season and definitely a quality reserve, but Real Madrid might find themselves selling him if Liverpool offer €20 million as The Sun is reporting. Cheryshev isn't probably worth that much, and players like Jesé, Lucas Vázquez or even Marco Asensio could replace him when needed.
Furthermore, Cheryshev himself knows that his chances with Real Madrid will be very limited. Apparently, he will be Cristiano Ronaldo's backup, and while Benítez tends to make a lot of rotations throughout the season, the Portuguese star will not sit on the bench as much.
All that being said, Real Madrid do not need the money. There has been no galáctico signing this year -- and there will not be one --, so they could perfectly keep Cheryshev if he is willing to stay and accept his role as a backup. It will all probably depend on Cheryshev's decision.