The 26-year-old was thought to have sprained ligaments in his right knee during his side's 1-0 victory over Livorno on Sunday and was sent to visit professor Richard Steadman in Colorado, United States, for tests.
And the player's agent has now revealed that Rossi, who has undergone surgery on the same knee on two previous occasions, will complete three weeks of rehabilitation before being able to put a timescale on his return to action.
"Now we need to wait three weeks before understanding how best to proceed and above all how long he’ll be out for," Andrea Pastorello told FirenzeViola.it.
"Professor Steadman found Pepito's knee was slightly swollen, so he could not make a guess as to the recovery time. He put that back to the next visit.
"Unfortunately any damage to the cruciate ligament was what worried us the most and today continues to worry us. If it was only the collateral ligament then there certainly would've been no need for an operation and at most two or three months out.
"This now leaves a big question mark over the whole situation that will only be resolved after the next visit.
"Obviously it's a difficult situation, above all psychologically. He'll have to wait three weeks and his spirits are very low at the moment.
"Now Pepito will remain in New York with our doctor for rehabilitation. Meanwhile, the club and I will evaluate what to do next. We'll only know more after the next visit.
"Unfortunately, damage to the cruciate ligament is what worried us the most."
Rossi has scored 14 goals in 18 Serie A appearances this season.