The coach wants Inter to be wary of the Partenopei's threat, while Erick Thohir discussed the chances of Mauro Icardi leaving San Siro in the summer
The Nerazzurri have enjoyed a better season under the coach than last year - when they finished ninth - but unlike the Partenopei, whom Mazzarri left last summer, they have failed to challenge for a Champions League spot.
The former Stadio San Paolo boss is well aware of the quality Rafa Benitez's men possess and insists he will be friendly with Napoli president Aurelio De Laurentiis should he bump into him, despite the war of words between them since his departure for San Siro in 2013.
"We're expecting a tough match," Mazzarri told reporters. "Napoli are a quality side, as their league position shows. They have quality throughout the side and are very dangerous on the break.
"We hope to get a good result. Every time we've been close to really taking off this season we've gone and picked up some strange results.
"If I run into De Laurentiis? I have no problem saying hello to people I've worked with. I had four fantastic years at Napoli."
Mazzarri was hesitant to shed light on rumours that Mauro Icardi could be leaving this summer, just a year into his Inter career, while revealing he has been planning behind the scenes for potential signings at the end of the season.
"Icardi is coming on lots and playing well. I won't discuss transfer rumours though," he continued. "It's not for the coach to comment on.
"I share my transfer views with the club every week - that's part of the job"
However, Inter owner Erick Thohir was more candid about Icardi's chances of a transfer from San Siro and insisted that reports that David Villa could be swapping Atletico Madrid for Serie A are far-fetched.
"Icardi is important for us," he told FC Inter News. "He will definitely be part of Inter moving forward in the future, just like Mateo Kovacic.
"There are no discussions taking place about David Villa. I was in Madrid for the press conference about the Inter-Madrid match, then we went to lunch with a Madrid delegation.
"Now I am back here, so we haven’t discussed the transfer market."
Inter sit fifth in Serie A with four games to go - two points behind Fiorentina in fourth and five points clear of arch-rivals AC Milan in sixth.