A deal to take the Argentina international to Stamford Bridge has not yet been finalised, but it appears he may have already played his final game for Milan.
Donnarumma, who produced a number of fine saves in Milan's victory at the Stadio Luigi Ferraris, is unsure why Higuain wants to move on just six months into his loan deal.
"If Higuain made this choice, there must be reasons, but he is a friend and I wish him all the best," Donnarumma told Sky Sport Italia.
Fabio Borini and Suso were restored to Milan's starting line-up from their 1-0 loss to Juventus in last week's Supercoppa Italiana, both getting on the scoresheet in a well-earned win for Gattuso's men.
Borini opened the scoring with a close-range finish before Suso converted off the inside of the post late on, as Milan moved up to fourth having previously failed to score in back-to-back away matches in the league.
Donnarumma conceded that Milan started slowly against Genoa, but the 19-year-old goalkeeper was pleased that his side resumed their Serie A campaign with all three points.
"The Supercoppa defeat hurt, but our objective is fourth place and we are up there. Now let's focus on the next match, this one's in the bag," he added.
"It wasn't a great start, but we suffered all together and that is the most important thing. We fought hard and our quality emerged eventually to win a very difficult match.
"There's a long time to go, but we'll do everything we can to achieve our objectives."
Milan's top-four mission will likely continue without Higuain in their ranks, but assistant manager Luigi Riccio is hopeful that others - such as Patrick Cutrone - can step up in his place.
"I want to underline the great performances put in by Patrick Cutrone in the Coppa Italia, Supercoppa and today," Riccio said. "He was exceptional in attacking the space, stretching the Genoa defence and working for the team.”