The 29-year-old's season is over after cruciate ligament surgery and on leaving the clinic Mexes revealed he had almost certainly played his last game for Roma.
"It's talked about a lot, probably yes," Mexes told reporters when asked if he was signing for Milan.
"But neither in Italy nor abroad will I find a team like Roma. Football is like that. Life makes you make other choices."
His Roma and France team mate Jeremy Menez, visiting Mexes in hospital, hinted he could also quit Vincenzo Montella's sixth-placed Serie A side.
"I don't know," the midfielder told reporters when asked if he would stay.
Mexes has long been linked with Milan in the Italian media but he will not be heading to the San Siro as a direct replacement for Alessandro Nesta, who has announced he will not retire at the end of the season.
The 35-year-old centre-back, troubled by injuries for years, said in a recent interview that he was almost at the end of his career but the former Italy defender has now made it clear he did not mean he would stop in May.
"I was misunderstood the last time," Nesta told Milan's TV channel. "I didn't say I was quitting at the end of the season. I'm close to the end but not at the end."
