The 31-year old is being linked with Tottenham in the Italian press and although Gonzaga did not name names, he did confirm that English clubs were certainly looking at the former Udinese and Brescia man.
"I cannot deny the rumours coming from England, I have always given to president Claudio Lotito the opportunity to deal with other clubs and then, once the agreement may be reached, to let me know," Gonzaga told Tuttomercatoweb.
"I think that it is unlikely Lotito would deny Stefano.
"Could he go abroad? It is something that could be taken into account, but he feels a major player with Lazio.
"Mauri wants to win with the Biancocelesti jersey, but if he get offers from abroad and the president told us to take them into consideration, we'll evaluate them.
"Mauri doesn't ask to go abroad, but we'll see if it will be offered."