Napoli director Giovanni Manna is said to have arrived in London on Tuesday to hold talks with a number of Premier League clubs.
The Italian outfit have made an official enquiry about Manchester United midfielder Scott McTominay, according to Corriere dello Sport.
The Red Devills are said to value the 27-year-old at around £25-30m and have no intention to send him out on loan.
McTominay's contract at Old Trafford expires in 11 months and he has also been linked with the likes of Tottenham and Fulham this summer.
Napoli have reportedly contacted Man United about potentially singing Scott McTominay
United are looking to offload either McTominay or Casemiro this summer so they can sign a new defensive midfielder, with the club interested in Paris Saint-Germain’s Manuel Ugarte.
Transfer pundit Gianluca Di Marzio also claims that Napoli are close to signing Gilmour from Brighton, having already reached an agreement with the 23-year-old.
Manager Antonio Conte worked with Gilmour at Chelsea, which is where the 23-year-old made his breakthrough.
Gilmour has impressed at Brighton so far, where he made 32 appearances in the league last season, and is expected to have two years left on his contract.
The Partenopei hoping to agree a deal of £10m plus £2m in add-ons.