The 51-year-old tactician left the Serie A runners-up after four years in charge to replace Andrea Stramaccioni at San Siro, with Chelsea's outgoing boss Benitez reported to be on his way to Naples in the next few days.
Napoli president Aurelio De Laurentiis backtracked on leaked comments that suggested he had already secured the Spaniard's services and Mazzarri kept his counsel when meeting reporters in Amalfi on Monday.
"Out of respect for the next coach there, I won't speak about Napoli any more," he is quoted as telling the Gazzetta dello Sport.
The Tuscan must now plot Inter's return to the upper reaches of Italian football after Stramaccioni steered the Milan giants into a dismal ninth place - a worst league performance since 1994.
As a result the Nerazzurri failed to qualify for Europe for the first time since the 1999-2000 campaign, meaning Mazzarri has traded another tilt at the Champions League with Napoli for a season of rebuilding at Inter.
He added: "We did extraordinary things at Napoli in the last few years and leaving the Azzurri bench was a difficult choice.
"It was emotional to collect my things from my dressing room at Castelvolturno (Napoli's training base), but you should always look forward in life.
"I thank the Napoli fans for all the love they showed me and I think I reciprocated their love by giving everything I had for the Azzurro cause."