Tomori was sent on loan to the Italian giants in January having fallen out of favour under old boss Frank Lampard.
The loan move included the option to make it permanent for a £27million fee.
And it appears the club are ready to push to make it happen, although they are eager to negotiate a lower fee with the Chelsea hierarchy.
Milan's vice-president Baressi told Gazzetta dello Sport: "We will do everything possible to sign him on a permanent deal.
"Two months are remaining until the end of the season, and it's not only up to Milan.
"Tomori is imposing himself with talent and determination. He has shown no fear playing in a new league.
"He can potentially become a great champion. I hope he lives up to expectations."
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!