The Argentina international is on loan at San Siro from this season but has been heavily linked with a move to Stamford Bridge in this month's transfer window.
Gattuso's team beat Sampdoria 2-0 in extra time to reach the Coppa Italia quarter-finals on Saturday, and afterwards the coach admitted he faced a fight to keep the 31-year-old Higuain at the club.
'We have a very open relationship, we say things to each other's faces,' Gattuso told Milan TV. 'There is great honesty. When a player makes certain choices, it becomes difficult to convince him otherwise. One can try.
'At the 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 the same attitude, which has never been lacking.'
Higuain, who has scored eight goals in all competitions for Milan this season, has been named in the squad that will travel to Jeddah in Saudi Arabia to face Juventus in the Italian Supercup on Wednesday.
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