But when the fierce rivals meet at Old Trafford on Monday evening, both will be searching for a first win after underwhelming starts to the season.
Liverpool have yet to lead after drawing their opening two games against Fulham and Crystal Palace, while Jurgen Klopp has had to contend with injuries and a red card for new £64m signing Darwin Nunez.
United have lost their opening two matches under Erik ten Hag, including a humiliating 4-0 defeat at Brentford.
Having lost their last two matches of 2021-22 under interim manager Ralf Rangnick, United are looking to avoid a fifth straight league defeat for the first time since a run of seven between January and March 1972.
With disgruntled United fans planning a fresh protest against the "failing ownership" of the Glazers before kick-off, it promises to be a lively night both on and off the pitch.
Will Liverpool kick-start season at Old Trafford?
If Liverpool's recent Premier League form over United is anything to go by, this game has come around at just about the right time for Klopp's side as they look to kick-start their season.
The Reds are unbeaten in their past eight top-flight matches against United, taking 18 points from 24.
Indeed, since United last defeated their rivals in the league in March 2018, they have sacked two managers [Jose Mourinho and Ole Gunnar Solskjaer], appointed one caretaker [Michael Carrick], appointed one interim [Ralf Rangnick] and appointed another permanent manager [Ten Hag].
Liverpool have scored 13 goals in the past three meetings, nine without reply in last season's two games.
Egypt forward Mohamed Salah has scored six goals in his last three matches against United.
Liverpool are looking to win four consecutive league games against United for the first time since January 2002, and are looking to win three straight away league games against them for the first time.
Worryingly for Klopp, who has seen his side drop four points from their opening two games of this season, Liverpool have conceded first in the past six league games.
Will they stop that trend at Old Trafford?
Ronaldo unrest & horrible form
When United hosted Liverpool last October, there was a negative atmosphere after their previous Premier League game ended in a 4-2 defeat at Leicester.
Ten months on and Liverpool's return to Old Trafford will coincide with another demonstration of supporter unhappiness after a heavy 4-0 defeat at Brentford.
The Brentford defeat moved the Manchester United Supporters Trust to release a strong statement at the way the club is being run.
"As we've always said, a fish rots from the head. And the ultimate responsibility for the terrible state of our football club must lie with its owners, the Glazer family," it read.
United have brought in Argentina defender Lisandro Martinez from Ajax in a deal worth up to £57m, Netherlands full-back Tyrell Malacia from Feyenoord for £14.7m and Denmark midfielder Christian Eriksen on a free since finishing sixth in the table last season.
They have also reached an agreement to sign Real Madrid's Brazil midfielder Casemiro in a deal that would be worth about £70m.
But their horrible form from last season has spilled into this with United taking just four points from a possible 24 - one win, one draw and six defeats - since Cristiano Ronaldo scored a hat-trick in a 3-2 win over relegated Norwich on 16 April.
Ten Hag said: "They just have to deliver. That is my obligation and them. When I talk about players, and I want to emphasise, I'm in the same boat as well. When we are not in the right attitude, I'm not as well. We win together, we lose together."
Ronaldo's absence from most of United's pre-season games fuelled speculation over his future after he also missed the club's return to pre-season training at Carrington.
He played the full match against Brentford having started the 2-1 home defeat by Brighton as a substitute
Ronaldo announced in the build-up to the Liverpool match that he will soon reveal "the truth" about his future after reading so many "lies" this summer.
Will the Portugal forward inspire United against the Reds as Ten Hag looks to avoid becoming just the second United manager to lose each of his first three games in charge of the club in all competitions, after John Chapman in 1921?
'Do we have a witch in the building'
While it is important to recognise the season is still in its infancy, Liverpool need a win after dropping four points from two games.
They will have to get it without Nunez, who is suspended following his red card for a headbutt on Joachim Andersen in the 1-1 draw with Crystal Palace last Monday.
"It's important we all recognise we are getting a 'work in progress' with Darwin - he recognises that himself," said Klopp when Liverpool announced the signing of the Benfica striker in June.
Nunez, 23, will also miss the home games against Bournemouth on 27 August and Newcastle on 31 August.
It is a setback for Klopp who has been without several players because of injury including Thiago Alcantara (thigh), Diogo Jota (thigh), Curtis Jones (calf), Joel Matip (groin), Roberto Firmino (foot), Alex Oxlade-Chamberlain (thigh) and Ibrahima Konate (knee).
"We have had a really tricky week," said Klopp. "Every day someone pulls up and you think 'what is going on here - do we have a witch in the building?'"
'United in bad shape'
Simon Stone, BBC Sport
Two seasons ago, this fixture had to be postponed when fans got into the stadium as a protest against the Glazer family escalated way beyond the scope of security put in place to deal with it.
Given United were on a 13-match unbeaten run on their way to a second-placed Premier League finish - and also went on to reach the Europa League final, little wonder there are fears around this particular rematch.
United have not been in as bad a shape as this for nearly 50 years, when they actually were relegated from the top flight.
Organisers have publicised the pre-match protests. It is hard to imagine that on a weekday evening during the holiday season, the attendance will be a big one.
United as a club need the protests to be peaceful but there will be a lot of nervous people until the game actually starts.