Azzurri president Aurelio De Laurentiis has admitted he would be interested in bringing the unsettled 22-year-old to the San Paolo as a strike partner for Edinson Cavani, or as a possible makeweight should City make a bid for the free-scoring Uruguayan.
AC Milan appeared to distance themselves from a rival approach for the Italy international when president Silvio Berlusconi described Balotelli as a "rotten apple", but Mazzarri is confident he could tame the capricious striker.
Quoted in La Repubblica, he told Radio Monte Carlo: "I do not know him personally. I spoke to him once a few years ago at a hotel in Sorrento.
"He made a good impression on me but only those who know him well can say what kind of problems he might create in training.
"I've got a bit of experience, though, and it would be stimulating to work with a talent like his, but I don't know if that would ever happen."
Azzurri president De Laurentiis had told Gazzetta.it: "Are City considering letting Balotelli go so they can move for Cavani?
"I would prefer to see Balotelli playing with Cavani here at Napoli.
"Teams tend to hold on to their best players in January. You take a big risk making big investments now.
"There is still time for us to bring in new faces but we must be cautious. On January 31 you will see what moves Napoli have made."
Milan had previously been mooted as Balotelli's likely destination, with the Rossoneri appearing to free up the necessary funds and space in their squad with the 15million euro sale of Alexandre Pato to Corinthians, but Berlusconi told reporters at the FIFA Ballon d'Or gala in Zurich that any approach was unlikely.
"The name of Balotelli never came into my thoughts, he is a rotten apple and could infect every group where he goes, even Milan," the former Italian prime minister said.
Balotelli's agent Mino Raiola responded through Sport Mediaset, saying: "Mario and I are saddened by what Berlusconi said.
"Berlusconi doesn't know him, everyone who does know him loves him. (Milan vice-president) Adriano Galliani knows him and loves him.
"If someone asks me to introduce Mario to Berlusconi then I will do so with pleasure."
Balotelli has been linked with a move away from the Etihad Stadium following a number of high profile incidents since he arrive in England from Inter Milan.
The latest occurred last Thursday, when he was pictured grappling with City boss Roberto Mancini.