The top-of-the-table clash at Anfield offers Arsenal, who face West Ham, and Chelsea, who host Aston Villa, the chance to gain ground.
AFP Sport picks out some of the key talking points ahead of this weekend's action:
Liverpool's league to lose?
Arne Slot's rampant Reds go into the weekend off the high of beating Real Madrid 2-0 to top the Champions League table.
Liverpool have barely put a foot wrong in the Premier League either, surging into an eight-point lead after just 12 games.
All three teams who have enjoyed a lead of eight points or more at this stage of the season in Premier League history have gone on to win the title.
City are there for the taking.
Winless in six matches, the English champions are physically and mentally "fragile", according to manager Pep Guardiola, who is experiencing the worst run of his career in the dugout.
"It has been, is being and will be a tough season for us. We have to accept it for many circumstances," he said.
Even at their best during a glorious era under the Catalan, City have failed to tame Anfield, with their last win there in front of a crowd coming back in 2003.
Amorim seeks home comforts
Amorim did not hold back after seeing Manchester United labour to a 1-1 draw at lowly Ipswich in his first match in charge last weekend.
"We are going to suffer for a long period," said the Portuguese coach. "This will take time, but I know we have to win games."
The visit of struggling Everton to Old Trafford offers the Red Devils the perfect chance to kickstart life under their new boss.
The Toffees (10) are one of only three sides to have scored fewer Premier League goals this season than United's 13.
Sean Dyche's men are just two points above the relegation zone and have not beaten United away from home since 2013.
United, who sit 12th, need to make the most of home advantage to move swiftly back up the table with daunting trips to Arsenal and City to come in two of their following three league games.
Villa hit the skids
Aston Villa are another side struggling for form. A 0-0 draw against Juventus in midweek extended their winless run to seven games in all competitions.
Unai Emery's men are still well placed to progress to the knockout stages of the Champions League in their first taste of Europe's elite competition for four decades.
But their European exertions are beginning to take a toll domestically. Villa have taken just seven points from their past seven league games to slip to eighth.
Next up is a difficult trip to Chelsea, who are flying high in Enzo Maresca's first season in charge.
The Blues sit third, ahead of Arsenal on goals scored, and could easily end the weekend as Liverpool's closest challengers should City fail to end their winless run at Anfield.
Arsenal have bounced back to form with comprehensive wins over Nottingham Forest and Sporting Lisbon and will go second for 24 hours at least with victory at West Ham on Saturday.
Fixtures (all times GMT)
Friday
Brighton v Southampton (2000)
Saturday
Brentford v Leicester, Crystal Palace v Newcastle, Nottingham Forest v Ipswich, Wolves v Bournemouth (all 1500), West Ham v Arsenal (1730)
Sunday
Chelsea v Aston Villa, Manchester United v Everton, Tottenham v Fulham (all 1330), Liverpool v Manchester City (1600)
