
Villarreal president Fernando Roig said Rossi, 20, will sign a six-year contract with the "Yellow Submarines" as they are known in Spain.
The digital version of the Marca daily said on Wednesday that Villarreal will pay United around nine million euros (12.33 million dollars) for the little Italian forward, who did well last season when on loan at Serie A side Parma.
Parma and several other Italian clubs were interested in Rossi, but the youngster opted for Villarreal, who will be in the UEFA Cup next season.
Rossi has the difficult task at Villareal of replacing Diego Forlan - another former Man Utd striker - who has moved on to Atletico Madrid.
Marca said that Villarreal are reportedly also interested in signing Fenerbahce defender Diego Lugano, 26, who created a good impression playing for Uruguay at the recent Copa America tournament in Venezuela.
Marca said that Villarreal are ready to offer Fenerbahce around six million euros (8.22 million dollars) for Lugano.