Gattuso has been a reported target of Russian side Anzhi in recent months.

"I don't think he will leave," Galliani said to Corriere dello Sport. "He has a contract with us for another season, and hence, he is not a free agent.

"Should a big offer arrive from the Russians, we will listen to it.

"However, I don't think he will go there, I think he will remain with us."

The 33-year-old Gattuso, who joined Milan in 1999, has made 27 league appearances for the Serie A leaders this season.

Milan beat city rivals Inter 3-0 on Saturday to go three points clear at the top of the standings with seven games remaining.