The relegated Liga side have indicated their intention to keep the Italian attacker, thwarting any potential summer move by Massimiliano Allegri's Serie A runners-up
The Rossoneri are in the market for a striker to fill the void left by the departure of Zlatan Ibrahimovic to Paris Saint-Germain, and the 25-year-old American-born Italian is the latest name to have been linked with a move to San Siro.
But following relegation from La Liga and the subsequent sale of Borja Valero and Gonzalo Rodriguez to Fiorentina, the Yellow Submarine are unwilling to part with yet another key member of their squad.
"There is nothing to say about Rossi to Milan," vice-president Jose Manuel Llaneza reportedly told Milannews. "This is the first time I've heard of it."
"Obviously, there is nothing that can be said about such rumours."
Rossi has endured a prolonged spell on the sidelines due to injury, rupturing his anterior cruciate ligament twice last season, and undergoing surgery three times.
Milan's desire to bring in a high-profile name has also seen them turn to former talisman Kaka, although the club have revealed that negotiations with Real Madrid have been put on hold.