Balzaretti, 31, is the subject of a bid from Roma.
"The interest from Roma is the most intense," President Zamparini told Radio Radio.
"Recently Juventus also stepped forward, but we'll see what happens. Federico told me if he had to choose a city to live in, then Rome would be fantastic.
"We can take several options into consideration, such as a paid loan or a permanent transfer with payments spread out."