Milan are in the market for a big name No9 and see an opportunity to prise Suarez away from Barca given his scratchy form.
Don Balon says an enquiry has been made, though Barca are yet to formally respond.
For his part, Suarez recognises leaving Barca for Milan would be a step down, but he hasn't ruled out the move as he struggles to shake his form slump.
Inside Barca, the Uruguay international's future is being discussed for the first time since his arrival from Liverpool. However, Suarez can still count on the full support of close friend Leo Messi.
Just last week, Milan coach Vincenzo Montella touched on his striker options.
Montella said: "Not everyone has a Gonzalo Higuain. The match was decided by a top player who created two goals out of nothing.
“Top players worth €100m won't come without the Champions League. I am happy with the transfer market we conducted."