Rossi, who has come back from two anterior cruciate ligament injuries to become Serie A's top scorer this season with 11 goals for Fiorentina, sat out training on Thursday morning and is unlikely to be risked in Friday night's friendly against Germany in Milan.
Enrico Castellacci, the head of Italy's medical staff, told www.figc.it: "He still has severe tonsillitis which is debilitating.
"He is taking antibiotics and we need to see whether his condition improves in the next few hours.
"We will do an assessment but, with regard to tomorrow's [Friday] match, there is little time.
"It will be the coach who makes the decision but it will be difficult (for him to play) if he does not improve a lot quickly."
If Rossi does not make it, coach Cesare Prandelli is likely to pair Mario Balotelli with Pablo Osvaldo in attack.