The 30-year-old had been placed a top of the Blues' wish list following the arrival of manager Maurizio Sarri, with the pair having forged a strong relationship from their time together at Napoli.
However, Milan are eager to bolster their attacking options in a bid to return to Europe's top table, following a four year absence from the Champions League.
According to Gazzetta dello Sport, the Italian giants have made their move to attempt to lure the striker to San Siro this summer having made an 'unofficial' offer of a four-year contract worth €4.5m-per-year - €2.5m less than his wage packet in Turin.
The Rossoneri are eager to ascertain Higuain's interest before tabling an official offer to Juventus - who have made it clear that they are not willing to part with the 30-year-old for anything less than €60m.
Higuain scored 23 goals in 50 appearances last term, more than Patrick Cutrone and Giacomo Bonaventura combined (18).
However, the report claims that Chelsea remain in pole position due to the presence of Sarri at Stamford Bridge and the club's ability to meet the player's requests - although no official bid has been tabled by the Blues.
Chelsea are prepared to let Alvaro Morata leave the club this summer following a disappointing debut campaign in the Premier League, and the funds from his potential move would be used to seal a deal for the Argentina international - with Chelsea eager to recoup as much of the £58m they paid to Real Madrid.