The 25-year-old has been out of action since October 2011 with a knee injury and is not expected to return for another five months.
"Roma? Rossi had given the all-clear to the move, but then it never quite materialised. There were several clubs who showed an interest, but at this moment we mustn't be in a rush," Federico Pastorello told Sky Sport Italia.
Rossi has scored six goals in 27 games for Italy.