The Argentina international left Italy for Paris St Germain in the summer of 2012 after five years shining in Serie A for Napoli - three spent under Mazzarri.
He was taken to France as part of an ambitious rebuilding project at PSG, but has found it difficult to produce his best in Ligue 1.
Talk of a January exit was been mooted, with Inter, Arsenal and AC Milan all said to be keen.
Mazzarri is, however, keeping his cards close to his chest, with the winter window not due to open for a few weeks yet.
He said of Lavezzi: "He's a great player and a great guy.
"He was sold to one of the most important clubs in Europe thanks to the three years of work.
"In terms of the market, let's finish the next game first, then we will make our conclusions.
"We could also remain as we are for this year, but it depends on what the club calls for at the end of the year.
"You have to understand when Milito and Icardi return, they are the first two attackers. I'm not talking about the market anymore because there are three important games that will help me assess the squad."