The Italian club’s president, Aurelio de Laurentiis, revealed his interest in the Colombia international following an injury to new number one Alex Meret, who broke his arm in training just six days after signing last month.
The Italian transfer window will close on Friday, one day ahead of the new Serie A season, so Napoli will have to move fast to get a deal over the line.
De Laurentiis told Radio Kiss Kiss Napoli: "There are four in contention: Ochoa, Mignolet, Ospina and [Ciprian] Tatarusanu.
"It is true that Ospina could arrive, we are negotiating, there are still some differences on the requests."
Ospina has been relegated to third choice at Arsenal with the summer arrival of Bernd Leno, and, as previously revealed by Goal, has also held talks with Turkish side Besiktas.
He moved to Arsenal from Nice after he impressed at the 2014 World Cup, helping his country reach the quarter-finals in Brazil and regularly featured in cup competitions under Arsene Wenger, including a starting berth in the 3-0 Carabao Cup final defeat to Manchester City last season.
He was understudy to Petr Cech in the Premier League however, and now finds himself further down the pecking order in north London.
Napoli, who finished second in Serie A last season, will hope to start a potential arrival in their first game of the season against Lazio on Saturday.