The 33-year-old turned down an move to Dagestan-based side Anzhi Makhachkala last month.
Gattuso’s agent, Andrea D’Amico, claimed on Thursday that the midfielder would be open to a summer move to the Russian Premier League.
“I have one year left on my contract with Milan,” Gattuso said. “Milan is my home and I feel very happy in this club.
“My agent cannot decide on his own, everything has to go via me.
“I reiterate it, I am happy at Milan.”