Brewster has been waiting patiently for his chance to shine at Anfield since graduating to the senior squad back in 2017.
Unfortunately, the 20-year-old has been unable to force his way into Jurgen Klopp's plans amid strong competition for places in attacking positions at Liverpool.
The likes of Mohamed Salah, Roberto Firmino, Sadio Mane and Divock Origi are all currently ahead of the England U21 international in the squad pecking order, which is why he has been restricted to just four competitive outings for the club to date.
Liverpool ultimately decided to send Brewster out on loan to Swansea in the second half of the 2019-20 campaign, where he managed to score 11 goals in 22 Championship appearances.
He returned to Anfield earlier this summer and impressed during pre-season, but is now being tipped to leave the club once again before the transfer window closes.
Sheffield United are reportedly eager to bring in Brewster on loan, but Goal has learned that the Reds would prefer to sell the young forward, with Crystal Palace also weighing up a swoop for his services.
Wilder has now revealed that the Blades are in contact with the player and Liverpool's CEO over a potential deal, as he looks to increase his options upfront at the start of the new season.
"I don’t know. I’m not going to mug everyone off by saying we haven’t spoken about Rhian," the Sheffield United boss told a press conference ahead of a meeting with Aston Villa on Monday.
A transfer update from the Gaffer 👇— Sheffield United (@SheffieldUnited) September 19, 2020
“The club has spoken to Liverpool. I’ve left that situation now for the CEO.
I’ll get my answers off him regarding Rhian, and other targets as well. We are looking in that position.” pic.twitter.com/rzla3wq5LF
"I’ve spoken to their manager and the CEO has spoken to the CEO. I’ll leave it up to him (Steve Bettis) now.
"We have a list of targets, though. We have to.”