Emil Danchev believes the Russia Premier League is "growing seriously" but insists that no formal offer has come for the 32-year-old.
"I have heard of interest from Russian clubs," ESPN quotes him as saying. "The Russian league is growing seriously, and should soon become one of the leading championships in Europe - so to play in that country would be interesting.
"Of course, much will depend on the decision of the Fulham hierarchy. But at the moment I do not know of any formal offers."
Berbatov has scored 13 goals in the Premier League for Fulham this season.