The semi-finals are usually two-legged affairs but will be played over just one match in this occasion, in the week commencing January 4.
The final had initially been scheduled for February 28 but has but isnow set to be played on 25th April at Wembley.
The Manchester clubs have won the last five finals between them, with United’s 3-2 win over Southampton in 2017 interrupting a run of dominance.
Pep Guardiola’s team are bidding to win the trophy for a fourth year in succession and a sixth time in eight years.
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Manchester City knocked their local rivals out at the semi-final stage last season and United boss Ole Gunnar Solskjaer said: “It is the worst game to lose probably, a semi-final.
Tottenham HotSpurs are bidding to lift the cup for the first time since a 2-1 win over Chelsea in the 2008 final.
They will be favoured to beat Brentford, although the Championship club have already knocked out four Premier League sides in Southampton, West Brom, Fulham and Newcastle.
Edinson Cavani and Anthony Martial goals sent Manchester United into the semi-finals of the Carabao Cup after a 2-0 victory over Everton.
Edinson Cavani Scored in the 88th minute to break the deadlock in their quarter-final clash on Wednesday night, while substitute Martial sealed the win with the last kick of the game at Goodison Park.
Brentford progressed to a first major cup semi-final in their history as they beat Newcastle 1-0 in their Carabao Cup quarter-final.
Never in their 131-year existence had Brentford made it to the last four of either the FA Cup or League Cup, but Josh Dasilva’s second-half goal (66) was enough to see the club reach that stage on Tuesday night.
Manchester City kept their Carabao Cup defence firmly on track after easing past Arsenal with a 4-1 victoryat the Emiates Stadium to book their place in the semi-finals.
Pep Guardiola’s side are now 18 games without a defeat in the League Cup as they bid to win the competition for a fourth straight time.
Tottenham remain on track for a first piece of silverware since 2008 after winning Championship side Stoke City 3-1 to reach the Carabao Cup semi-finals.
Tottenham HotSpur’s boss Jose Mourinho has now reached the League Cup semi-finals for a fifth time, going on to win the competition on each of the previous four occasions his side have got to this stage (2004-05, 2006-07, 2014-15 and 2016-17).