The San Siro side have set their sights on the French wideman as they aim to add an extra attacker to their squad before the end of the transfer window
The San Siro side have already secured the services of Adil Rami, Keisuke Honda and Michael Essien this winter, while they are also on the verge of signing Adel Taarabt on a loan deal.
However, recently-appointed head coach Clarence Seedorf is keen to add some more fresh blood to his squad and he sees the 25-year-old Biabiany as the ideal signing.
"Over the course of the evening, Parma director Pietro Leonardi met with Adriano Galliani at the Giannino restaurant," a statement on the Milan website reads.
"Galliani has acknowledged that Seedorf is a big admirer of Biabiany.
"Leonardi, meanwhile, is neither optimistic nor pessimistic about a potential transfer."
Biabiany, who has made 19 appearances in Serie A this season, has previously played for Inter, Chievo, Modena and Sampdoria.