Daily Star Sport understands United have reached an agreement with the Reds in the last 24 hours to sign Brewster, who will now undergo his medical with Chris Wilder’s side.
The 20-year-old also needs to finalise personal terms ahead of his switch to Bramall Lane.
His permanent Liverpool departure comes as a surprise given the solid form he displayed on loan at Swansea earlier this year, registering 11 goals in 22 games for Steve Cooper’s men.
Yet the Premier League champions have ensured the door will remain open for their academy graduate to return if he comes on leaps and bounds in Sheffield.
In the deal to sell him to the Blades, they have included a buy-back option that can be triggered at any point over the next three years.
Should they regret their decision to offload him permanently, Liverpool will be able to bring him back to Anfield for a pre-arranged price.
The Reds have also inserted a 15 per cent sell-on clause in the deal, meaning they will also benefit financially if he lands a lucrative move elsewhere.
Brewster was expected to leave on loan again this summer after thriving at Swansea in the second half of last season.
However, with Roberto Firmino an indispensable for Jurgen Klopp upfront - and with Diogo Jota, Takumi Minamino and Divock Origi ahead of him in the pecking order - Liverpool have decided his future should lie elsewhere.
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The striker has racked up just four appearances since emerging from their youth ranks in 2017, just two years after joining from Chelsea’s academy.
He will be joining a Sheffield United side in desperate need of goals, having drawn blank in their first three Premier League games of the season.