The Blades have only four senior centre-halves on their roster – leaving them vulnerable after a return to a back three earlier this season.
Ben Davies’ recent absences have exacerbated the problem, with Paul Heckingbottom frustrated as targets James Hill and John Souttar went elsewhere.
And Rhys Williams, the Liverpool youngster, is a player of interest for Heckingbottom, alongside his Anfield teammate Nathaniel Phillips.
But who is Williams, how highly do Liverpool rate him and what has boss Jurgen Klopp said about him?
A good grounding at Liverpool
Williams, still only 20 years old, joined Liverpool’s academy at the age of 10. He won the FA Youth Cup with the Reds in 2019 and enjoyed his first taste of senior football that year with a loan move to Kidderminster Harriers, signing a long-term deal at Anfield in 2020.
His Liverpool debut came in a League Cup tie against Lincoln City, partnering Virgil van Dijk at centre-half in a 7-2 win, and he made six appearances in the Champions League before making his Premier League bow – a 2-1 win over Tottenham Hotspur at Anfield after van Dijk was injured.
He finished last season with 19 appearances under his belt, often partnering Phillips at the heart of defence during the season run-in, and was loaned out in the summer in a bid to accelerate his development.
What happened at Swansea City?
Williams joined Swansea in the summer to some fanfare but his loan was cut short recently, with Liverpool seemingly unhappy with the youngster’s lack of gametime.
He made only seven appearances, and five starts, for Russell Martin’s side. But the Swans boss believes it was still a worthwhile move.
"I think he has grown a lot in his time here," Martin said. "He's frustrated he didn't play more but I think we leave on good terms. I am sure Liverpool will be disappointed he hasn't played more, but loans are not easy at this level.
"He goes with everyone's best wishes. He has been fantastic member of the squad character-wise, the way he has trained, he has had a smile on his face.
"He needs to go back to Liverpool and force his way in there or maybe go back out elsewhere, we'll have to wait and see."
Could that be an issue at Sheffield United?
Possibly. United’s back three is relatively settled and Williams’ best chance of getting into it would possibly be on the left – a big ask for a right-footed centre half, albeit one who did play on the left at times for Liverpool last season.
Chris Basham is right up there as a first-choice pick and John Egan wouldn’t be too far behind him. But with a heavy fixture schedule facing the Blades in the second half of the season, there is a real chance injuries, suspensions and even Covid-19 absences may yet hit them hard.