Both Harry Redknapp and Kenny Dalglish are interested but the report claims his former club inserted a buy-back clause in the deal that took Rossi from the Red Devils to Villareal.
However, Inter are said to also be involved and the diminutive striker reportedly prefers a move to Italy after failing to make the grade when playing under Sir Alex Ferguson.
The 25-year-old has been transformed since his move to Spain and last season scored 32 goals for the Yellow Submarine.
This year has not gone to plan, however, as Rossi suffered a torn cruciate ligament in October and his recovery schedule means participation in Euro 2012 with Italy is uncertain.
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