The Giallorossi, who are currently under the guidance of Aurelio Andreazzoli, are believed to be looking for a new coach this summer, despite the interim boss steadying the ship since Zdenek Zeman's departure in February.
Meanwhile, Mazzarri's future at the Stadio San Paolo is also unclear, with some reports suggesting that he could take a sabbatical after four years at the helm.
The 51-year-old's agent was reportedly spotted at Roma's training ground recently, but he has distanced himself from taking over at the Stadio Olimpico.
"Should I be flattered by Roma interest? You say this, I know nothing," Sky Sports News quotes the Italian as saying.
Mazzarri guided Partenopei to the Coppa Italia glory last season.