Juventus tried to sign the former Manchester United striker last summer and Russian sides Rubin Kazan and Zenit St. Petersburg have also been linked with the hitman.
Rossi’s agent, Andrea Pastorello, has confirmed that a return to Italy is likely.
“After the summer, Juventus no longer contacted us,” Pastorello told Tuttomercatoweb.com.
“I think he will remain with Villarreal for now. There have been some important requests for him from Luciano Spalletti, as well as from Rubin, but we continue to turn them down.
“Rossi prefers the classic European leagues and he wants to return to Italy in June.”