Ospina is widely expected to leave Arsenal before the end of the month, having fallen further down the pecking order at the Emirates Stadium following the arrival of Bernd Leno.
Alex Meret only joined Napoli from Udinese this summer, but the stopper broke his arm shortly after arriving, and the Italian outfit will sign another goalkeeper before the August window slams shut.
De Laurentiis has confirmed that Ospina and also Liverpool's Simon Mignolet are both in the mix.
"There are four in contention: [Guillermo] Ochoa, Mignolet, Ospina and [Ciprian] Tatarusanu. It is true that Ospina could arrive, we are negotiating, there are still some differences on the requests," he told Radio Kiss Kiss Napoli.
Ospina has only made 11 Premier League appearances for Arsenal over the last three seasons.