Martin O'Neill had reportedly been lining up a loan move for the Argentine, who has made just one Serie A start for the Rome outfit this season.
Despite apparent interest from the Black Cats, and several other European clubs, Zarate's agent Luis Ruzzi has revealed the 25-year-old is in no rush to leave his current employers.
Speaking to Calciomercato.it, he said: "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 experience of playing in England, having enjoyed a six-month loan spell with Birmingham City in 2008.