The 20-year-old has established himself as an important part of the Championship side's squad as the Blades target a second promotion in as many years.
Brooks's impressive form has also led to a spot in the Wales senior squad, his full debut against Panama on Tuesday seeing him put in a man-of-the-match performance.
Even though United only recently tied Brooks down to a new four-year deal in October, The Mirror claims that Liverpool and Spurs continue to circle around the youngster.
Tottenham boss Mauricio Pochettino has a penchant for developing British talent and is eager to work with the Welshman, according to the report.
Brooks has made 17 appearances for the Blades so far this season.