Last season's runners-up have been faultless so far this term, but they take on a Blades outfit that has impressed on their return to the top flight with eight points from six games.
Five points clear at the top of the table after six games is a position which any team would gleefully accept, although if Liverpool needed reminding about the quality of those chasing them then they were last weekend when champions Manchester City blew Watford away in an eight-goal evisceration.
The result piled extra pressure on Jurgen Klopp's side for their trip to Chelsea a day later, but the red machine kept on rolling with a 2-1 triumph in West London, showing maturity to see the game out under late pressure.
Liverpool have now won 15 top-flight games in a row, extending their own club record once again, and Manchester City's run of 18 a couple of seasons ago is now the only time in English football history where a team has been on a better run of victories in the top division.
Indeed, records seem to tumble on a weekly basis for this Liverpool side, although Klopp will know that their status as one of England's greatest ever teams - a label the stats suggest they deserve - will depend almost entirely on the silverware they accrue along the way.
The Premier League is, of course, the big one, but they have been disappointing in domestic cup competitions over the past couple of seasons and Wednesday's 2-0 victory at MK Dons would have therefore been a welcome continuation of their winning ways, albeit with an entirely different XI.
A fourth-round game against Arsenal is their reward - a match which will bring an end to a difficult run of games coming up. After this weekend, Liverpool face Leicester City, Manchester United and Tottenham Hotspur in succession, as well as Champions League outings against Salzburg and Genk.
The standards Liverpool and Man City set last season mean that any dropped points are hugely significant, but considering that upcoming run anything other than a win in Saturday's early kickoff would be a major blow for the as-yet perfect Reds.
The visitors will certainly be significant favourites heading into the contest considering they are now 23 league games unbeaten - the second-longest run in their history - while they have won each of their last 12 matches against newly-promoted teams, conceding only four goals in that time.
It is safe to say that Saturday's match could be a daunting one for Sheffield United, then, although Chris Wilder's men have already proved that they are not the type to get cowed by coming up against top-quality opposition.
Since returning to the top flight for the first time since 2007, the Blades have notably come from two goals down to draw with Chelsea at Stamford Bridge and just last weekend ended the fine home record of Liverpool's Merseyside neighbours Everton.
The visit of the European champions is another step up from that again, though, and interestingly it is in front of their own fans where their most disappointing results have come so far this season.
United have lost three of their last four home games in all competitions, most recently slumping to a 1-0 defeat at the hands of League One Sunderland in the EFL Cup third round on Wednesday night.
It is an issue which must be at the top of the agenda to fix if the Blades are to get the points they need to stay in the division, although three of their next four home games come against Liverpool, Arsenal and Manchester United, so it will be difficult to turn that form around.
In general, though, United will be very happy with their start to the campaign - certainly if you had offered them a mid-table spot at this juncture then they would have taken it - and should they pull off a shock against Liverpool on Saturday then they could even temporarily move as high as third place.
Not since 1990 have United lost three top-flight home games on the bounce - and not since 2013 in any division - and there is more cause for optimism in the fact that Liverpool have never won a Premier League match at Bramall Lane, one of only three stadiums where that is the case.
In a week where Klopp was crowned The Best FIFA Men's Coach, Saturday's hosts can also lay claim to having a manager of high repute; since the start of the 2014-15 campaign, no boss has won more English league games (125) or earned more points (426) in the top four tiers than Wilder.
Sheffield United Premier League form: DWLDLW
Sheffield United form (all competitions): LWDLWL
Liverpool Premier League form: WWWWWW
Liverpool form (all competitions): WWWLWW
Klopp made the full 11 changes to his side for Wednesday's EFL Cup match in Milton Keynes, so expect a swathe of first-team players to come back into the fold for this one.
The likes of Virgil van Dijk - narrowly beaten by Lionel Messi in the FIFA Best awards on Monday - Mohamed Salah and Roberto Firmino are all expected to return to the starting lineup, while Sadio Mane should have recovered from the dead leg he suffered against Chelsea last weekend.
At least one of that front three has scored in all but one of their ongoing 15-match winning streak, netting 27 goals between them in that time, but should Mane not recover in time then either Adam Lallana or Alex Oxlade-Chamberlain could be pushed into a more advanced position.
James Milner is another who started on Wednesday and could be in line to feature again following an impressive performance, although Andrew Robertson will return in the left-back spot and both Fabinho and Georginio Wijnaldum will expect a recall in midfield.
Naby Keita made a welcome return with over an hour in midweek, but Divock Origi is a major doubt while Xherdan Shaqiri, Nathaniel Clyne and newly-crowned FIFA Goalkeeper of the Year Alisson Becker are still sidelined, although the latter revealed that he is closing in on a return.
Callum Robinson was the only player to start both the win over Everton and the Sunderland loss, so like their visitors United are likely to make sweeping changes to their most recent XI and could even name an unchanged team to last weekend.
One aspect which will have pleased Wilder so far is the goals being spread out throughout the team - all seven of their strikes this term have been scored by different players - but he will also be looking for one of his strikers to establish himself as the main goal-getter.
Sheffield United possible starting lineup:
Henderson; Basham, Egan, O'Connell; Baldock, Lundstram, Norwood, Fleck, Stevens; McBurnie, Robinson
Liverpool possible starting lineup:
Adrian; Alexander-Arnold, Matip, Van Dijk, Robertson; Henderson, Fabinho, Wijnaldum; Salah, Firmino, Mane
Head To Head
Saturday's match will be Liverpool's first trip to Bramall Lane since the opening day of the 2006-07 Premier League season, when only a penalty from returning hero Robbie Fowler rescued a point for the Reds.
Fowler scored two more spot kicks as Liverpool ran out 4-0 winners in the reverse fixture at Anfield in February 2007 - the most recent meeting between these two sides in any competition.
Liverpool have never won a Premier League game at Bramall Lane in three previous attempts and are without a victory in their last six visits across all competitions, stretching back to a 3-1 triumph in August 1990.
We say: Sheffield United 0-2 Liverpool
Sheffield United have been disappointing at home so far this season, and the visit of Liverpool will be their most difficult test of the campaign so far. The Reds are a winning machine at the moment and we are backing them to make it 16 in a row in relatively comfortable fashion.
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