Liverpool will retain a 15 per cent sell-on clause for the 20-year-old and a buy-back clause that is valid for the next three years.
Brewster will undergo a medical in Yorkshire on Friday and will then finalise terms ahead of signing for Chris Wilder’s side, although it is unclear whether he will be available for this weekend’s game at Arsenal.
Up to six Premier League clubs have expressed an interest in the forward – including Aston Villa, Brighton, Newcastle and Crystal Palace.
Liverpool are prepared to let their academy product leave in order to get more first-team football – while also needing funds to cover the purchases of Thiago for £25m and Diogo Jota for £45m.
Sheffield United are yet to score in the Premier League after their opening three games of the season, while Brewster recorded ten goals in a six-month loan spell at Swansea in the second part of last season.
He returned in the summer to make a substitute appearance in Liverpool’s Community Shield defeat to Arsenal and missed the crucial penalty in the shootout.
Sky Sports assess Brewster’s attributes and explain why the Liverpool striker, 20, is set to be a star of the future in English football.
“He just looks very comfortable and with the composure that he shows in front of goal, he is lethal,” says Andrews. “His general build-up play maybe needs to be worked on but there’s going to be aspects of every part of his game that slightly need to be worked on.
A selection of Rhian Brewster’s best goals for Swansea in the EFL Championship
“The biggest thing he’s got going for him is the fact that he’s an instinctive finisher. He doesn’t thrash at things, he’s very composed and he has a knack for heading as well.
“He can’t overpower 6ft 2in centre halves, he has to out-cute them. He has to get in between areas and he does that very well.”