Les Aiglons are the surprise early leaders in Ligue 1 and have impressed despite losing key forwards Hatem Ben Arfa and Valere Germain in the summer.
Despite signing Mario Balotelli, adding extra quality in January could prove crucial to their title push and it has been rumoured they may look to dip into the market.
Lavezzi previously played in France with Paris Saint-Germain but moved to the Chinese Super League in January to ply his trade with Hebei China Fortune.
However, he has recently been linked with a potential move to the Allianz Riviera and Favre says he would be interested if the Argentine became available, although he admits to being surprised about rumours.
"I was not aware," he told Le Figaro. "He's a good player. There was Paris, of course, but I remember his period with Napoli. He was good."