The Nice left-back has impressed for club and country, and the Serie A giants are thought to be ready to start a tug-of-war for the Argentina international's signature
The Argentina international has impressed for the Ligue 1 club since joining from Boca Juniors in July 2011, and representatives from both Serie A giants were thought to be in attendance at the South American nation's last game against Switzerland.
Marcelo Trapasso has discussed the 24-year-old's future and feels it would be no surprise should Monzon move to Italy.
"AC Milan and Juventus interested in my client? I have heard about it, and I cannot rule out that there is an interest," the representative told Calciomercato.
"At the same time they are two clubs with which I am on good terms and I have not received any official offers, and I know Nice haven't either.
"Executives of the two clubs were in Switzerland watching him? Yes, I know they were in Bern, but I can not guarantee that they were there for Fabian, although of course we feel that Italy would be a welcome destination.
"I repeat, the talk surrounding Fabian does not surprise me, but at the same time, for now there is nothing concrete.
"Obviously much will depend on what happens in the French league: If Nice remain in Ligue 1 he could stay, however, if they are relegated, then the departure of Fabian would be a fact."
Monzon's side are currently 17th in the league standings.