The 19-year-old came through the youth system at his current club and made his first-team debut last year, while he earned his first cap for Portugal last month.
Neves has now made 36 appearances for Benfica, scoring once and providing two assists, including 16 outings in all competitions during the 2023-24 campaign.
The teenager's performances this season have led to a host of speculation surrounding his future, with both Man United and Manchester City said to be among his list of admirers.
According to Record, the 20-time English champions are considering making an attempt to sign him in January due to the growing interest in his services.
There is believed to be a £103m release clause in Neves's contract, but there have been claims that he could be allowed to leave his Portuguese club for around £61m.
The youngster has featured on 10 occasions in Portugal's top flight this season, while he has also played three times in the Champions League.
Neves is now seemingly firmly in the plans of Portugal head coach Roberto Martinez and will be bidding to be a part of their squad at next summer's European Championship.
Man United are currently well-stocked in the middle of midfield, but there have been claims that Casemiro could leave the club during the January transfer window.
Casemiro, who is out until at least Christmas with a hamstring issue, is Man United's leading goalscorer this season with four in all competitions.
However, there has been criticism surrounding his defensive performances this season, and a number of Saudi Arabian clubs are believed to be keen on his signature.
Kobbie Mainoo, 18, is seen as an important player for the future, but midfield is an area that the club allegedly want to address in 2024.
Man United are also expected to sign another striker and a centre-back next year, with the club continuing to overhaul their squad under the management of Erik ten Hag.