Saints completed a club-record deal to bring in the Uruguayan after a protracted pursuit during the summer.
Zanzi told Tele Radio Stereo: "Ramirez knew that we would have sold him only with certain conditions. Such conditions happened only at the end of the market and so we had little time to act in the market.
"Despite the difficulties we were able to do a nice job by taking Gilardino.
"Ramirez accepted the Southampton offer because he couldn't refuse.
"Were there proposals from Italy for Ramirez? The economic situation of Italian football means at the moment Italian clubs are struggling to make similar proposals to those coming from abroad.
"Gaston eventually opted for the Premier League."