The Blues were heavily linked with a move to the Portuguese winger during the summer, but the Rossoneri rejected their approach.
The Premier League giants were willing to pay around £65m, but the Italian outfit did not want to sell their star asset following their recent takeover.
However, the situation could change at the turn of the year, particularly with the 23-year-old playing hardball over a new deal.
Leao has a deal at Milan until the summer of 2024, and the Serie A giants could be tempted to sell him for a higher fee.
Chelsea are prepared to try again for him in the mid-season transfer window, and it is claimed that a package of around £87m could convince the Italian champions.
The Portuguese has been excellent for the Rossoneri this season, contributing four goals and seven assists in nine appearances.