The Rossoneri have been heavily linked with making an offer for the 25-year-old ever since his current club Villarreal were relegated to the second tier of Spanish football.
With the transfer window due to close at the end of the month, agent Federico Pastorello has admitted that the centre-forward is eager to secure a switch to Serie A.
"Milan? I don't know if contact with the Rossoneri has been made, but Rossi would definitely say yes if he was approached by Milan," he told Sky Sport 24.
"For Giuseppe Rossi the transfer market will start in the last few weeks of the transfer window. He wishes to play in Serie A again and I expect a call from Italian clubs.
"He could be very useful to Napoli and Roma. Inter also need younger players in their squad. Juventus lacks a top player and Milan have to replace the strikers that have left the club."
Rossi joined Villarreal from Manchester United in 2007.