Tottenham are also eyeing the former Manchester United trainee.
Roig told Sport: "We have not had offers from any club. The player is on holiday but he has said to me that he wants to be here, that he is happy, and I also want him to stay with us.
"(Rossi is) a key player, an important player and we are counting on him and his goals for next season."
Roig also dismissed interest in midfielder Borja Valero from Atletico Madrid, who is under contract with Villarreal for another four seasons, and is hopeful of agreeing a new deal with out-of-contract midfielder Marcos Senna.