The 21-year-old, who currently plays for the Spanish champions' second side Castilla, impressed in pre-season for the senior team and has caught the eye of many sides in Europe.
Zingarevich has spoken out about his club's interest in the young Russian talent, and says that the player knows about it.
He said: "Our scouts watched Cheryshev for Castilla against Barcelona B. Denis played 20 minutes.
"I'm not guaranteeing that he will go to Reading, but it's possible. And Denis knows about it."The Spanish giants have said that they are not looking to sell the winger though, who has had a lot of interest from Spartak Moscow and three other russian clubs.
The London side are likely, however, to request a loan deal if the player's performances continue to be impressive for the Spanish second division side.
Zingarevich also revealed that the club had two Russian players on trial, 17-year-old Sergey Kundik and Nikita Khaykin, who came through Chelsea's youth system, but that neither could acquire a work permit.