Should Real Madrid fail to sign a suitable replacement in time for the start of next season, the Russia international will stay with Los Blancos beyond this summer, according to Spanish newspaper AS.
It was reported earlier this month by talkSPORT that Liverpool were preparing a £14 million offer for Cheryshev, who Brendan Rodgers has identified as the ideal replacement for the wantaway Raheem Sterling.
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But Rafael Benitez will only sell the 24-year-old, who is currently on holiday in the Dominican Republic, to his former employers if another right-sided winger arrives at the Bernabeu beforehand.
At this moment in time it's unclear who will occupy the right wing position in Real Madrid's first team from the start of next season.
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Bale keen to switch positions
Gareth Bale played there last season, but it's understood the Wales international has asked Bentiez to deploy him elsewhere on the pitch following a string of ineffective performances in that position last season.
Bale is optimistic about his future under Benitez, who made the effort to visit the former Tottenham star during the recent international break, but it's unclear whether his wish will be granted by the Spanish coach.
In order to accommodate Cristiano Ronaldo, Karim Benzema and Bale in the same attacking line-up, the latter will almost certainly need to continue playing on the right flank.
Cheryshev a level below Bale and Sterling
Cheryshev impressed on loan at Villarreal last season, scoring seven goals in 40 appearances, but he is not in the same class bracket as Bale.
It could also be argued that he's not at the same level as the £50 million-rated Sterling, who looks increasingly likely to join Manchester City this summer, but Rodgers clearly feels the Russian could do a job for the Reds in the Premier League.
Rodgers will be under intense pressure to ensure he makes the most of the Sterling money later this summer.
The Northern Irish manager clung on to his job at the end of last season; however, the knives will be out for the Reds' boss if his new signings fail to hit the ground running.
The players Rodgers brought to Anfield with the money generated by the sale of Luis Suarez all flattered to deceive last term - and the Liverpool manager can ill-afford to repeat the same mistakes this summer.
Liverpool fans: would you be happy if Denis Cheryshev replaced Raheem Sterling this summer? Let us know by leaving a comment in the box below!