The 25-year-old has been out of action with a raptured cruciate ligament since October.
The former Manchester United striker has long been linked with a move to Italy.
Rossi’s agent Federico Pastorello told Sky Sport 24: “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.
“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.”
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?