While the Frenchman has contributed three goals and five assists for Marseille this season, he is currently due to be out of contract in the summer.
Unless he agrees fresh terms with the Ligue 1 side before the end of 2020, the 27-year-old will be free to discuss a transfer with foreign clubs.
Maldini has acknowledged that Milan may be unable to turn down a chance to sign the playmaker, highlighting that Thauvin would represent value for money.
The club legend told Telefoot: "He's player who will be at the end of the contract, so he's an interesting player from an economic point of view.
"He's a player of a high level. It's not exactly the prototype of the players we have brought here in these two years, regarding his age.
"What he always says, however, is that the right mix is created by many young players with some more experienced who can give a little more. Surely, it's a profile that must be followed."
Either side of a disappointing spell at Newcastle United, Thauvin has established himself as a key man at Stade Velodrome. body check tags ::