The 27-year-old has been repeatedly linked with a move away from Old Trafford this summer with the transfer deadline less than one week away.
According to a report from journalist Fabrizio Romano, the Serie A club have maintained their interest in signing McTominay but are yet to meet United's valuation.
Antonio Conte's side are said to have tabled a proposal worth £21m, but United are standing firm and are looking a fee in excess of £25m.
Manchester United have reportedly received an offer for Scottish midfielder Scott McTominay from Napoli
McTominay's current deal at Old Trafford is set to expire at the end of the season.
Fulham had also shown an interest in McTominay but are now believed to be out of the race after their completing their signing of Sander Berge from Burnley earlier this week.
McTominay had looked set to depart his boyhood club last summer, with then-West Ham boss David Moyes reportedly keen on signing his compatriot.
Ultimately though, the deal was not completed and the midfielder remained at United for Erik ten Hag's second season at the club.
Despite being limited to just 18 Premier League starts throughout the campaign the Scotland international managed a career-best 7 league goals, including vital winners against Brentford and Aston Villa.
The midfielder also featured in every game of United's run to the final of the FA Cup last season, starting in the final as they defeated Manchester City 2-1 at Wembley.
Should McTominay make the move to the Stadio Diego Armando Maradona this summer he could soon be joined by a familiar face.
The Serie A side have reportedly agreed a fee that could be worth up to £18m with Brighton to sign Scotland international Billy Gilmour.