Russian Premier League sides have until Thursday to complete any transfer business, with their window about to slam shut.
Gradel is among those being considered by a number of clubs, with tentative talks already underway.
One concrete offer has been put to St Etienne, who may be tempted to cash in if the terms are right.
They snapped Gradel up from Leeds United in 2011 and have seen him net nine times in 50 Ligue 1 appearances.
The 25-year-old's representative Cyrille Timwo Monthe told Izvestia: "Several clubs from Russia are really interested in Gradel's services, but I don't want to disclose exactly which.
"What is more, one Russian club have already made a specific proposal."