The Russian side are considering making an attempt to sign one of Los Blancos' promising talents, but it is understood that no official talks have been held
The 21-year-old joined Los Blancos in 2002 after spending seven years following Cheryshev senior through clubs like Sporting Gijon and Buros.
The winger has so far been unable to break into Real Madrid's first team, and his father has revealed that the player might be tempted to jump ship in search of regular football.
"We will wait and see what happens next. If talks between the clubs progress and we receive a contract offer, we will have to look at it before deciding what to do," Dmitri Cheryshev told Izvestia.
"Of course, it is a great honour to be linked with Zenit. All I have heard is that Zenit are very interested in Denis.
"However, I must admit there have not been any talks or concrete offers yet."