Carlo Ancelotti's side have already signed one goalkeeper already this transfer window, having completed a £10m deal for Udinese shot stopper Alex Meret last month. However, the 21-year-old fractured his arm in pre-season training only a few weeks later, meaning that I Partenopei have to dip into the market once again.
And according to Italian sports journalist Gianluca Di Marzio, the Serie A club are looking at Premier League back-up goalkeepers Ospina and Mignolet, alongside Standard Liege and Mexico number one Guillermo Ochoa.
However, the fact that Napoli have already signed Meret this summer means that the Italian side are only looking for a temporary loan deal for either goalkeeper, and not a permanent transfer, which could complicate the negotiations.
Ancelotti's side also have Greek goalkeeper Orestis Karnezis and youngster Nikita Contini as back-up shot stoppers to Meret, so are in no rush to conclude a deal.
Arsenal's Ospina is wanted by many clubs around Europe after being deemed surplus to requirements by new Gunners boss Unai Emery. The Colombian's chances of first-team football in north London have been damaged by Bernd Leno's arrival from Bayern Leverkusen over the summer, with the German international set to compete alongside Petr Cech and Emiliano Martinez for a starting spot in Emery's side.
And Mignolet's situation is very similar to his Arsenal counterpart, having been pushed down the Liverpool pecking order by Jurgen Klopp following the arrival of Brazilian goalkeeper Alisson from AS Roma.
Should a move for either Premier League goalkeeper prove unsuccessful, then Napoli could turn to Mexican international Ochoa, who is Les Rouges' first choice goalkeeper. The 33-year-old has played in each of Liege's four games so far this season.