The forward has been starring in the youth team at Ewood Park since making his debut at the age of just 14. Rovers are braced for interest from several Premier League clubs, and United are believed to be among them.
Livesey has registered 125 goal contributions across Blackburn's academy set-up in a single season, a return that has made him one of the most talked-about young players in the country.
Like fellow academy prospect JJ Gabriel, of United, Livesey made his debut for Blackburn's Under-18 side when he was just 14 years old.
Livesey was born in Salford, meaning United were one of his local clubs growing up.
Manchester City, Liverpool, Chelsea, Tottenham and Arsenal have also been credited with interest, along with Brighton and Newcastle United.
Blackburn are keen to keep hold of their academy star, but the Championship club will not be able to offer him a professional contract until he turns 17.
That means any Premier League club moving for him now would only have to pay compensation for his development, rather than negotiate a full transfer fee.
Rovers have a strong recent record of producing top-level talent, with Crystal Palace midfielder Adam Wharton among the graduates of their academy system.
Manchester City, Manchester United and Liverpool are understood to be the leading contenders for Livesey's signature, with all three clubs entering the new season under fresh management.
City have appointed Enzo Maresca, Manchester United are working under Michael Carrick on a full-time basis for the first time, and Liverpool have installed Andoni Iraola as their new manager, giving each club a reason to invest in the next generation.
For now, Livesey remains focused on his development at Ewood Park, though Blackburn are braced for the interest to intensify significantly over the coming months as clubs look to secure his signature before he is old enough to sign professional terms.