Rossi is eager to leave Villarreal before the summer market shuts.
Federico Pastorello told Sky Sport 24: "Has there been contact with Milan? I do not know, but maybe with Milan having bought Cristian Zapata there might have been a discussion between the clubs.
"We can classify it as a hypothesis. If Milan were interested then there would be no doubt that it would please Rossi. The availability to Milan of the boy would be total.
"I think there will be some movement for Rossi, and not only from Italian clubs, having also seen him play for Manchester United and explode at Villarreal. But he would be perfectly happy to play in Serie A.
"I feel that his transfer could be sorted late in the summer market and then by the end of January he should be available and could make the second half of the season."