The Italy international was plagued by a recurring knee injury during the last campaign but has been linked with a move to the Rossoneri in the current transfer window.
The 25-year-old has endured a tough year after rupturing a ligament in October, and then suffering a repeat of the injury when he returned to training with the Yellow Submarine in April.
His injuries restricted him to just 14 appearances in all competitions last season for the club, and without him Villarreal was relegated from La Liga in May.
Despite his lengthy spell on the sidelines, some of Europe's top teams retain an interest in signing the player, including Milan. His agent, Federico Pastorello, confirmed to Sky Sport 24 that the forward would welcome such a move.
"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," Pastorello said. "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."
The Italian has made 192 appearances for the Spanish side since joining from Manchester United in 2007.
Follow GOAL.COM USA on