Rigg, 17, is widely regarded as one of the best teenage talents in English football, with a host of major clubs believed to be tracking him with a view to a future move.
Manchester City, Liverpool, Chelsea, Barcelona and Real Madrid are all believed to be keen on the midfielder, but according to HITC Sport, there is also significant interest from Man United.
The report claims that scouts from the 20-time English champions view Rigg as 'the next Roy Keane' and are desperate not to miss out on his signature.
Man United are believed to have made contact over a potential move over the summer, but the youngster signed his first professional contract at the Stadium of Light.
Man United 'desperate' to win the race for Rigg
Sunderland are allegedly bracing themselves for offers, and there is a chance that a deal could be agreed in January with a view to a transfer occurring next summer.
Borussia Dortmund are also said to be in the race, and the German outfit were famously Jude Bellingham's choice when the Englishman left Birmingham City to sample life abroad.
Rigg has already made seven appearances for Sunderland this season, and he scored his first goal of 2024-25 for the Black Cats in their 1-0 success over Middlesbrough on Saturday afternoon.
"My first goal of the season and hopefully many more, I didn't have enough numbers last year and I am trying to improve on that," the midfielder said after scoring against Boro.
How will the situation play out?
Man United are in the market for the best young talent in world football, and it is not too difficult to understand why there is so much talk surrounding Rigg.
The youngster has already made 32 appearances for the Black Cats, scoring four times, and the fact he is playing consistently in the Championship at his age and in his position is so impressive.
Rigg's contract at the Stadium of Light is due to run until June 2027, but it is highly unlikely that he will still be at Sunderland next season, even if the club are promoted to the Premier League.
Man United famously missed out on Bellingham to Dortmund, but the Red Devils simply cannot let this opportunity pass them by, as Rigg as the potential to be a constant in the Man United midfield over the next decade, and he could join Kobbie Mainoo in a very exciting engine room.