The Italian Serie A giants, who are enjoying a good season under Antonio Conte, want to bring in Duran in the summer.
The 21-year-old Colombian only signed a new deal at Villa Park in recent months.
He has a contract until 2030, which will make any potential transfer hugely challenging.
Italian journalist and Napoli expert Ciro Venerato stated: “There is a player that De Laurentiis, Manna and Conte are crazy about, he is Jhon Durán from Aston Villa, he costs €40 million.
“Napoli have already had two talks with the player’s agent and will soon have a conference with the English club shortly.
“He is a profile that has been evaluated and already promoted by the whole of Calcio Napoli.
“We need to understand the availability of Aston Villa and the agreement on the evaluation.
“We also need to understand if Napoli, in order to beat the competition, can take him as early as January and leave him in England until June or whether to make an operation that contemplates the summer market.”