The 25-year-old has been strongly linked with a move to the Premier League in recent weeks, but no official movement has yet been made for the former Birmingham City attacker.
Luis Ruzzi told calciomercato.it: "There isn't any market news and our position is clear - we are ready to continue together with the club. Mauro has another year-and-a-half contract with Lazio and we want to stay, unless we find a good solution.
"Rumours about Genoa, Besiktas and Sunderland? There have been contacts with some clubs and it is true that I met the [Genoa] president Enrico Preziosi, but it is up to the clubs to find an agreement. We'll see what happens."
Zarate has also played for Inter Milan.