The San Siro giants are actively seeking a new recruit up-front, with Leonardo's side having already failed to sign Wolfsburg goal-machine Edin Dzeko, former Arsenal striker Emmanuel Adebayor and Sevilla hit-man Luis Fabiano.
Rossi, an American-born Italian international, made just five league appearances for Manchester United before moving to Spain in 2007, where he has been a revelation in la Liga, bagging 23 goals in 57 league outings.
And the diminutive front-man also recently starred for the Azzurri at the Confederations Cup in South Africa, netting twice against the United States.
His impressive form was believed to have interested Serie A duo Milan and Juventus, while both Manchester United and Manchester City were thought to be keen on bringing the forward back to English shores.
Speculation that Rossi could be on his way out of Villarreal intensified over the weekend after the Yellow Submarine agreed to sign Internacional starlet Nilmar for a club record fee.
And, according to Radio 24 and Radio Radio, Milan's official webpage announced the signing of the 22-year-old on Monday, only for the story to quickly vanish again.
Whether the club's website was the victim of a mischievous hacker, or the story was published by an over-eager Milan employee remains to be seen.
NEWS: Rossi expected to stay in Spain
NEWS: Rossi set for Old Trafford return?
