The 23-year-old striker, who made three starts for Newcastle and eight substitute appearances in 2006/7, has spent the last three years in Spain with Villarreal.
Having joined the academy ranks at Manchester United while still in his teens, he was sent on loan to St James' Park, and moved to Spain in 2007.
Giuseppe Rossi: "I hope to return to Italy in January.
"Fiorentina or Juventus? I don't know if they were interested over the summer.
"Any team will be fine, we will just have to see what happens.
"The most important thing, I repeat, is that I come back to the Italian championship."