Rossi in the dark over United future
Rossi will have to play the waiting game to find out where he will play next season.
"Parma have made an offer and are awaiting a response from Manchester United," said the player's agent Andrea Pastorello.
Rossi joined Parma on a six-month loan deal from United and was pivotal in helping the Ducale outfit retain their Serie A status.
Although the United youngster is rated highly at Old Trafford, Sir Alex Ferguson's long-term plans for the Italian could change with the arrival of West Ham's Carlos Tevez.
The Argentina forward is expected to join United after the Copa America, a move which could see Rossi leave Old Trafford.
"I think with an offer of 10-12m euros (£6.7-8.1million), Manchester United could be tempted to let Rossi leave," added Pastorelli.