The Serie A giants are on the cusp of losing Kalidou Koulibaly, who is expected to join Chelsea this summer with a deal worth €40m in the works.
Napoli are already moving in the market to identify and secure a replacement for the experienced defender.
Fiorentina defender Nikola Milenkovic has been offered to Napoli and Fenerbahce’s Kim Min-Jae has also been targeted.
And according to Italian broadcaster Sportitalia, Bailly has emerged as a potential target for the Serie A giants as well.
Napoli have carried out contacts and enquiries over the possibility of taking the Manchester United defender to the Stadio Diego Armando Maradona this summer.
Manchester United are open to selling the Ivory Coast defender as part of their plans to reshape their squad under new manager Erik ten Hag.
But Bailly, who impressed in a friendly against Liverpool on Tuesday, is believed to be keen to stay and fight for a place in the team.
Napoli are yet to make a concrete move or table an offer, but Bailly is a defender they are closely tracking.