Cadena Cope journalist Paco Gonzalez (h/t Alex Harris of the Daily Star) has said the attacker is likely to be on his way to England on the final day of the January window, with Liverpool the potential destination for the Russia international.
The player admitted he is finding life difficult at Los Blancos, constantly overlooked to represent the starting XI, as reported by Rhys Turrell of the Daily Star. Cheryshev said in November: "Of course, you want to play more but the situation is not easy. You have to be strong and look forward."
Here is a video of the attacker's best moments in Spanish football:
Liverpool manager Jurgen Klopp said he expects to be alert as the transfer window concludes, per Harris: "We are always busy and checking possibilities. If something happens we will see. There's nothing to say."
According to Hugo Cerezo of Spanish newspaper Marca, the Russian was looking for a loan move in January, and Liverpool were only one of the clubs interested in signing him up—along with Everton and Villarreal.
Cerezo indicated a key motivation for Cheryshev was to temporarily move away from the Bernabeu so he can get more first-team minutes and compete for a place in the Russia squad for the forthcoming Euro 2016 tournament.
Cheryshev has failed to start a game for his club this season, rising only five times from the bench in La Liga and the Champions League, according to WhoScored.com.
Real coach Zinedine Zidane admitted the forward might be on his way on the final day of the window, per AS:
AS English @English_AS
Zidane: "We'll see tomorrow but yes, Cheryshev could leave. He's a great player but he needs to play"2016-1-31 21:52:30
Liverpool are also tipped to move for Juventus striker Morata, offering the Spaniard an increased chance of first-team football.
Italian outlet Calciomercato (h/t Aaron Flanagan of the Mirror) said the attacker could be tempted to leave the Old Lady after losing his place to Paulo Dybala, and Liverpool lead the race to capture his talents.
Morata has failed to scale the heights of previous campaigns, and the arrival of Dybala in the summer has limited his match time.
Liverpool are desperate to add a genuine No.9 after the continued absence of Daniel Sturridge and the abject failure of Mario Balotelli.
Cheryshev and Morata are at the stage of their careers where they need a theatre to perform at. They also need the guarantee of regular first-team football.
Morata would answer Klopp's immediate needs as he looks for an alternative to Christian Benteke in attack, but the preference would be to get Sturridge fit and firing every week.
Liverpool need to do business on the final day if they have true aspirations to finish in the European spots in the Premier League, and high-class additions such as Cheryshev and Morata would help the Reds fulfil their objectives.