However with the Red Devils on a pre-season tour of Asia, they will have to bide their time in negotiating a potential deal for the striker.
"We had a meeting at [exclusive resort] Folgaria with Rossi's agents," said Parma president Tommaso Ghirardi.
"We discussed the situation but we know we must wait for Manchester United to return from their tour of Asia before we know a little more about Giuseppe's future."
Italy Under-21 star Rossi, 20, scored nine goals in 16 Serie A matches in the second half of last season to keep Parma in the top flight after a relatively ineffective stint in the Premiership with Newcastle.
Rossi is regarded as a bright prospect and so Sir Alex Ferguson may well prefer to keep him at Old Trafford, although he has reinforced his attacking options this summer with Nani and Anderson.
United finish their schedule in the East on July 27th against Guangzhou Pharmaceutical. They play Shenzhen on Monday 23rd having already hammered Seoul 4-0.