Higuain moved to Milan in the summer following Cristiano Ronaldo's arrival at Juve, and despite his reputation as one of the most dependable goalscorers in Italian football, he has struggled at the San Siro.
Rumours linking the player with a possible move to Chelsea have surfaced as a result, although Gattuso said on Friday he wants the former Napoli and Real Madrid man to stay where he is, per Sean Wilson of Goal.
"Higuain? Gonzalo has presented himself well," he said. "I hope that he stays here as long as possible; if it's not like this, we'll see. It will not be a problem for me."
According to Jason Burt of the Daily Telegraph, the Blues are exploring a possible loan for the striker. Higuain's brother and agent, Nicolas, was reportedly in London on Thursday to hold talks with Chelsea representatives.
Burt added that Chelsea will consider sending out Alvaro Morata on loan if they can secure a replacement, and Higuain is their priority target in the mid-season window.
Blues boss Maurizio Sarri worked with the striker during their time together at Napoli. In their final season together, the Argentinian forward set a new goalscoring record in the Italian top flight:
Sarri was asked about a possible move for the striker at his own press conference on Friday and said Chelsea need to make some signings:
On the back of that incredible campaign, the forward earned a move to Juventus and helped the team win two Serie A titles in his two terms. However, the summer acquisition of Ronaldo meant there would be a shift in the side's attacking onus.
Milan appeared to be the beneficiaries, although the 31-year-old has not been able to find his best under Gattuso, netting just six times in 15 games in Serie A.
Despite his struggles, a loan move for Higuain would possibly make sense for Chelsea. The MailOnline's Tess Derry commented on how much Morata has faltered when tasked to lead the line this term:
Aside from his recent stint at Milan, Higuain has been prolific throughout his time in Italy:
The concerns come from the fact that the forward has looked a little past his best over the past year. Additionally, the pace and robustness of the Premier League mean strikers often require a physical presence to thrive up top; that's something Higuain has never had, instead relying on his penalty-box instincts.
Still, Chelsea need a regular goalscorer to take some of the burden off the shoulders of Eden Hazard. In a functioning side and under a manager he knows well, Higuain may yet have it in him to make an impression in English football.