Arsenal will take on Newcastle United in the other semi-final.
The Reds sit five points clear of second-placed Chelsea, who can close the gap with a win against Brentford at Stamford Bridge on Sunday.
Manchester United manager Ruben Amorim insists he did not speak to Manchester City about replacing Pep Guardiola at the Etihad Stadium before making his move to Old Trafford.
Manchester's crisis-hit clubs face off in the Premier League when City host United on Sunday
Mohamed Salah's second-half double was not enough to extend Liverpool's seven-game winning run in all competitions as they failed to win for just the third time in 21 games under Arne Slot.
West Ham produced a clinical away performance to beat resurgent Newcastle 2-0 on Monday, easing the pressure on beleaguered manager Julen Lopetegui.
Mikel Arteta's men have now picked up just one point in their past three games as their title push quickly runs out of steam.
Manchester City's second successive draw in the league was especially frustrating as Arsenal moved level on points with them with a last-gasp 4-2 win against Leicester a few hours later.
Enzo Maresca made 11 changes from the team that beat West Ham 3-0 on Saturday but could still start around 400 million pounds ($533 million) worth of talent.
Chelsea suffered fresh frustration after blowing the lead in a 1-1 draw against Crystal Palace, while Newcastle beat Tottenham 2-1 on Sunday.
Ex-Liverpool manager Jurgen Klopp had only won two of his 11 away games against Manchester United.
Newcastle defender Kieran Trippier announced his retirement from international football on Thursday after winning 54 caps for England.
Noni Madueke hit a hat-trick as Chelsea crushed Wolves 6-2 to give Enzo Maresca his first Premier League win as Blues boss.
The Argentine was axed this week after just a year in charge despite steering Chelsea to a sixth-place finish and Europe next season.
Tottenham missed the chance to move into the Premier League's top four after a 1-1 draw at West Ham, while Newcastle were also held 1-1 by Everton on Tuesday.
Eddie Howe's men are languishing in 10th place in the Premier League with 10 games to go and any hope of the club's first major trophy since 1969 is over for another year.
Bernardo Silva scored twice as Manchester City beat Newcastle 2-0 to reach the FA Cup semi-finals on Saturday, while Coventry struck twice in stoppage time to stun Wolves 3-2.
Manchester United are aiming to derail Liverpool's bid for a quadruple and salvage a difficult second season for Erik ten Hag in Sunday's FA Cup quarter-final.