Jurgen Klopp revealed last week that a decision on the young striker’s future at Liverpool has not been taken, but Brewster could leave Anfield soon.
Brewster spent the second half of last season on loan at Swansea City and has again been linked with heading out on another loan stint.
But it appears that Liverpool are open to selling the young striker for a substantial fee, with several Premier League keen to grab at the opportunity.
Sheffield United have been monitoring the situation for several weeks with a view to taking the 20-year-old striker to Bramall Lane in the ongoing transfer window.
And it has been claimed that the Blades are working hard behind the scenes to work out a deal to sign Brewster from Liverpool.
Chris Wilder is a big fan of the young striker and is desperate to sign the Liverpool academy graduate.
But Sheffield United are not the only ones chasing him and clubs such as Crystal Palace are also interested in Brewster.
The young striker has been keen for his long term future to be at Liverpool, but it appears that he could leave the Reds on a permanent contract before next month’s transfer deadline.