The Bulgarian, who joined Fulham from Manchester United last summer, has scored 13 goals in 30 league appearances for the capital outfit this season.
"I have heard of interest in Berbatov from Russian clubs in the past and I still hear of them today," he told Izvestia.
"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."
Zenit St Petersburg are reportedly leading the chase for the forward.