Mediocre displays in draws against Fulham and Crystal Palace mean Juergen Klopp's side are already in the bottom half of the table, and injuries and a three-game suspension for new signing Darwin Nunez add to the sense of unease at Anfield.
Incredibly, Liverpool's early-season problems look trivial compared with those of their arch-rivals Manchester United.
For the first time since 1992, United are bottom of the Premier League after losing their opening two games against Brighton and Hove Albion and Brentford.
Thirty years ago they recovered to win the title, but currently not even the most optimistic United fans will believe they can realistically challenge for the top four, let alone think of challenging reigning champions City.
For a few hours early on Wednesday, United's fans dared to dream that Tesla founder Elon Musk was planning to buy the club, only for the billionaire to admit later on that his Twitter message was just a joke.
British chemicals magnate Jim Ratcliffe's apparent interest in buying in to Manchester United offers some hope for United's fans desperate for an end to the Glazer-family ownership.
But for now, the only thing on their minds will be avoiding what could be humiliation at the hands of a Liverpool side desperate to get their own season up and running.
United's performance against Brentford last weekend, when they conceded four times in the opening 35 minutes, was one of the most humiliating in the club's illustrious history.
New manager Erik ten Hag looked crestfallen on the touchline and the Dutchman surely could not have imagined quite how big a challenge he faces to revive United's fortunes.
Including the end of last season, United have now lost four successive Premier League games, scoring once and conceding 11 times.
Liverpool will be licking their lips, having beaten United 5-0 away and 4-0 at home last season.
Ten Hag's problems are so numerous his head will be spinning. Keeper David de Gea was a liability against Brentford, as were most of the defenders in front of him, while Cristiano Ronaldo gives the impression of wanting to be elsewhere.
United clearly need several quality signings but have so far failed badly in the transfer market with the clock ticking.
While it seems unlikely, victory would put United above Liverpool in the table and former Liverpool striker John Aldridge is wary of gloating about the problems up the road.
"Everyone is laughing at the state of United at the moment with their team, behind-the-scenes drama and the state of their ground," Aldridge told the Liverpool Echo.
"This game will be like a cup final for them. They will not have much else to play for this season other than beating Liverpool and Man City due to being so far behind as a club.
"If they win against us, they will go above us. That is a crazy situation to be in given how badly United are playing."
Before Monday's clash, Manchester City and Arsenal will both be looking to maintain their perfect starts.
City are at Newcastle United on Sunday, allowing Arsenal the chance to go top if they win at Bournemouth on Saturday.
Tottenham Hotspur, one of six teams on four points, begin the weekend programme on Saturday with a lunchtime kickoff against Wolverhampton Wanderers while Chelsea are at Leeds United on Sunday.
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