Higuain is Maurizio Sarri’s number one choice to replace Alvaro Morata, who is expected to leave Stamford Bridge this month.
Milan, however, don’t want Higuain leave in January without a replacement.
The deal will also be complicated, because the 31-year-old is on loan at San Siro from Juventus.
Despite the speculation, Higuain was picked to play against Sampdoria in a 2-0 win on Saturday, though he made little impact and Gattuso made it clear that his head was elsewhere.
“We have a very honest relationship, we say things to people’s faces. There is great honesty.
“When a player makes certain choices, it becomes difficult to convince him otherwise. One can try.
“At this moment, he is a Milan player and we’re holding on tight. I don’t know what will happen.
“We are honest with each other and I want him to maintain this attitude, which has never been lacking thus far,” Gattuso told Milan TV after the game.
During his press conference, he added: “I’ve talked to him a great deal, but it’s hard to give advice, because the career of a player only lasts 13-14 years. It’s his mind, not mine.
“I haven’t figured out what Higuain is unhappy with, because I see him look content and involved in the locker room atmosphere. We’ll see what happens. If it was up to me, I’d keep him at my house and feed him my dinner.”