20-year-old Luis is on the radar of several European clubs, despite not yet being a regular for Benfica.
And he is reportedly tempted by a move to Milan, where he believes he would get more game time.
Record states that the Rossoneri are ready to pay €3m for a two-season loan with an obligation to buy for €30m.
It would mean a €33m investment in total for Milan on the promising defensive midfielder.
Benfica value Florentino at €40m, which means Milan may have to improve on their offer to have a chance of signing him.
Florentino made 18 appearances across all competitions last season, 10 of them in Portugal’s Liga NOS.