Vincent Kompany's side let a one-goal lead slip in a 2-1 loss to West Ham United last weekend, while discontent around Bramall Lane grew as the Blades went down 3-1 to Bournemouth.
Match preview
An unwanted slice of English football history had already been written by Burnley before the visit of West Ham, as Vincent Kompany's men had become the first team to lose their first six home games of a Premier League season, and the Turf Moor curse continues to bedevil the crestfallen Clarets.
Jay Rodriguez's penalty early in the second half would seemingly bring an end to Burnley's home hoodoo, but a Dara O'Shea own goal on the 86-minute mark preceded a last-gasp Tomas Soucek winner for the Europa Conference League winners, as doom and gloom reared its ugly head for the hosts once more.
While Kompany's job appears to be safe for the time being, the Manchester City legend may be worried about the prospect of a P45 if the Clarets fall short for the eighth time at home in the 2023-24 Premier League season this weekend, to a direct relegation rival no less.
The Championship winners' paltry tally of four points sees them remain at the foot of the division and with an unassailable five-point gap to 17th-placed Luton Town - who were their most recent victims on October 3 - at this moment in time, and it is now seven defeats on the bounce for Burnley in all tournaments.
Burnley are already the first Premier League side to begin a season with six straight home losses, but they could now become the first team in the entire English Football League to endure an eight-game streak of such defeats at the start of a campaign. although they could hardly have been given a friendlier fixture to snap that horrendous sequence.
With a third of the season played, Kompany is the bookies' second favourite Premier League manager to be sacked after Sheffield United counterpart Paul Heckingbottom, who was forced to listen to a cacophony of boos from the Bramall Lane faithful as Bournemouth travelled back to the South Coast with a priceless three points.
Two Marcus Tavernier efforts either side of a Justin Kluivert strike rendered Oli McBurnie's late goal inconsequential while also ending the Blades' brief purple patch, which had seen Heckingbottom's men defeat Wolverhampton Wanderers and draw with Brighton & Hove Albion prior to the international break.
A 10th defeat from 13 Premier League affairs this season leaves Sheffield United only a point better off than Burnley in 18th place, but the Blades cannot clamber to safety with a win this weekend given Luton's four-point cushion, and 34 goals conceded remains the worst defensive record in the top flight.
Shipping goals at an average of over two-and-a-half per game, Heckingbottom's team have unsurprisingly failed to keep a Premier League clean sheet so far this season and have only found the back of the net four times on the road, a paltry tally that all other 19 top-flight teams can better.
A Johann Berg Gudmundsson brace proved decisive as Burnley bested Sheffield United 2-0 at Turf Moor in the Championship last term, although the Blades had run out 5-2 winners at Bramall Lane earlier that season and have only been beaten in one of their four Premier League affairs with Kompany's disjointed crop.
Burnley Premier League form:
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Burnley form (all competitions):
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Sheffield United Premier League form:
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Team News
Prior to Burnley's loss to Sheffield United, Kompany revealed that Lyle Foster would be taking some time off from football due to mental health struggles, although he stressed that the 23-year-old was receiving the "best care possible".
Experienced midfield cog Jack Cork is also likely to sit this one out after picking up an unspecified problem in training, while Arijanet Muric has been battling an infection but may return to the matchday squad on Saturday.
James Trafford should retain his place in goal for the time being, though, while Sander Berge will reunite with Sheffield United only a few months on from swapping Bramall Lane for Burnley in the summer transfer window.
As for Heckingbottom's team, there has been little movement with the visitors' long-term absentees, as Chris Basham (ankle), John Egan (ankle), Daniel Jebbison (illness), Rhian Brewster, Tom Davies and Rhys Norrington-Davies (all thigh) will sit out the trip to Turf Moor.
Jayden Bogle and Vinicius Souza only lasted until half time against Bournemouth after recovering from recent knocks, but the pair are expected to be given the green light to reprise their roles on Saturday, where McBurnie has made his case to return to the XI.
James McAtee's spot in the final third could come under threat from the fit-again McBurnie, while Anel Ahmedhodzic should be thrust back into the rearguard, potentially at Bogle's expense if George Baldock reverts to a wing-back role.
Burnley possible starting lineup:
Trafford; Vitinho, O'Shea, Beyer, Taylor; Gudmundsson, Berge, Brownhill, Koleosho; Amdouni, Rodriguez
Sheffield United possible starting lineup:
Foderingham; Ahmedhodzic, Trusty, Robinson; Baldock, Souza, Norwood, Hamer, Thomas; Archer, McBurnie
We say: Burnley 1-1 Sheffield United
Victory is not beyond the realm of possibility for either Burnley or Sheffield United this weekend, but both managers will be fully aware of the possible implications of defeat at Turf Moor.