The former centre-back took charge of Partneopei in 2009 and has led them to Champions League football during his tenure.
Mazzarri has seen his team go unbeaten in their first seven fixtures and sit second in Serie A on the same points as Juventus.
However, he has refused to rule out an exit from the Stadio San Paolo.
"I live one day at a time," Football Italia quotes the 51-year-old as saying. "On occasions I hear and see things that make me want to quit, to just give up.
"After the Italian Super Cup loss to Juventus in Beijing I had a desire, a real desire, to resign.
"Could I stop at the end of the season? Yes, that is possible."
Despite expected interest from Serie A's bigger clubs, Mazzarri, who replaced former Italian international Roberto Donadoni, does not believe that he has to trade up to achieve his goals.
"I don't feel as if I need to coach a club like Juventus, Inter or Milan to say I've made it," he added. "I understand that you, traditionally, tend to win more with those teams, but winning means something else.
"To save Reggina from relegation with so many deducted points meant more to me than winning."
Reggina had incurred an 11-point deduction following the 2006 Italian match-fixing scandal.