The former Villarreal striker is recovering from a knee injury sustained in last month's 1-0 win over Livorno.
Further scans have since revealed that the Italy international, whose career has been plagued by knee issues, does not require surgery.
Rossi witnessed his team-mates reach the Coppa Italia final with a 2-0 win over Udinese on Tuesday, securing a 3-2 triumph, with club president Andrea Della Valle dedicating the success to the 27-year-old.
"I have been told of the dedication from Della Valle. It brings me so much pleasure," Rossi told Firenzeviola.it.
"I was thrilled to see the semi-final on television. I spoke with some of the directors on this extraordinary achievement.
"And when I return, which I hope will be as soon as possible, I want to repay all that confidence that Fiorentina have had in me.
"With patience, hard work and dedication I will return to play.
"Where will you see Giuseppe Rossi come May? On the field, at the (Stadio) Olimpico."
