Rossi is set to be out of action until 2013 after it was announced on Monday he needed two separate operations on his injured knee.
A statement on the Villarreal website on Monday confirmed the 25-year-old will have two sets of surgery on the knee which is set to sideline him for up to 10 months. The first operation was performed by Colorado-based Dr Richard Steadman last week, and the next one is scheduled to take place this summer.
The statement read: "The first operation successfully took place last Friday, April 20. Once he has recovered from this surgery - in an estimated time period of four months - Steadman will perform the corresponding operation on the anterior cruciate ligament, which usually requires around six months of recovery.