Manager Jurgen Klopp has been keeping tabs on the 20-year-old midfielder since the beginning of the new season, and could make a £10m offer in January, as reported by the Mirror.
Other interested parties in Brooks include Arsenal, Newcastle and West Ham, who all like what they have seen so far from the youngster, who recently earned a call up to the Wales senior side for their final two World Cup qualifiers.
Brooks made his debut for the Blades 14 months ago in an U23s match against Leicester in the EFL Cup, and just 15 appearances later, he now finds himself recognised as one of the hottest young properties in English football.
Blades boss Chris Wilder is keen for Brooks to stay at the club this season, and sees him as someone with a big part to play in their promotion bid.
He said: "We are building something here and, of course, there will be casualties along the way. But David won’t be going anywhere in January."