According to Sky Italia (h/t Calciomercato), Milan have already held discussions with Higuain's brother and agent about a potential switch. Chelsea are also reported to be keen to land the striker, although Higuain is said to be tempted by the prospect of signing for another Italian team.
It's added that the Argentina international is not happy at the club after they signed Cristiano Ronaldo from Real Madrid earlier in the window seemingly as a way to sell him.
Higuain moved to Juventus from Napoli in the summer of 2016, becoming the third-most expensive player in history at the time. During his two-year spell he's been a success, continuing his prolific form in Serie A and helping the team win two titles in the process.
However, the player will understandably be a little concerned about the arrival of Ronaldo. It would be a huge surprise if manager Massimiliano Allegri didn't build his attack around the Portuguese next season.
Italian football writer Adam Digby hasn't ruled out the prospect of the pair working together yet:
Stylistically, there are similarities between the players. Both have developed into penalty-box predators.
For all the fine work Higuain has done for Juve, Ronaldo has long been one of the best players in the world.
Higuain, as such, may be faced with finding a new club this summer and any team that did land him would be securing a fine player, as these figures illustrate:
As noted by Calciomercato, while Milan have been having financial difficulties as of late, the club are said to be hopeful of resolving them this month.
Chelsea would represent an intriguing option, too, as new manager Maurizio Sarri has shown previously he is capable of getting the best from Higuain. When the two worked together in 2015-16 at Napoli, Higuain scored 36 Serie A goals, a record for the competition.
Despite that, Chelsea author Mark Worrall admitted he would have concerns about spending big money on the player:
Mark Worrall @gate17marco
Of all the incoming Chelsea transfer deals being touted around, the key one I have an issue with is paying £53 million for & offering a 3-year deal to Higuain. He's 31 next birthday & had a Morata-style goal drought last season. Buying a player for what he once was is foolish.
Now 30, Higuain may not have many years left at the highest level, and that would undoubtedly be a worry for any potential suitors. Even so, he's someone who has never relied on a burst of pace or brute strength, plus his goalscoring instincts remain razor sharp.
For Milan the acquisition would be a coup, especially given a number of their centre-forwards struggled last season. For a team pushing to get back in the UEFA Champions League again, the acquisition of Higuain could be a catalyst for them.