The Blades are desperate to add more goals to their team for this Premier League season.
Brewster reportedly could sign for the club, provided they agree on a buy back clause that allows Liverpool to get him back for a reasonable fee.
They will offer £17 million for the player and include the clause.
Their chase for a striker is hotting up, as Chris Wilder's team has not scored in three games.
If the deal goes through, the Reds could sign back Brewster for roughly £40 million.