The defender, who mainly operates at left-back, only moved to the Stadio Olimpico last summer but could now be on the move again.
The Portuguese defender worked under current Napoli manager, Maurizio Sarri, during his time at Empoli and his former boss is thought to be keen to work with him again.
A knee injury meant that Rui was unable to make his debut for current side Roma until January last season and that was partly to blame for, the 26-year-old, making just nine appearances in all competitions last campaign.
However during his time at Empoli, Rui played in almost every game and his pace and dribbling ability caught the eye of Roma last summer.
Rui's agent: "Roma will have to find a replacement & the two parties will need to find an agreement. Mario #Rui will go to Napoli".— Everything Napoli (@NaplesAndNapoli) June 26, 2017
Rui's transfer cost the team from the Italian capital just over £5m and n
It has already been reported that Rui's agent, Mario Giuffredi, met with Roma's hierarchy in the week and it is understood that the left-back has told them that he wants to leave for Napoli.
It has also been suggested that the defender has agreed personal terms on a contract with Napoli, that is expected to run until 2022, with higher wages than he currently earns in Rome.
Roma are said to be keen to sell as they already have sufficient left-backs in the squad, such as Juan Jesus, if they cannot secure a direct replacement for Rui.
As a result, an agreement between the two parties is expected to be agreed upon within the coming weeks.