Two-time winners Arsenal booked their place in the last four by beating Sunderland 5-1 on Tuesday.
In the other semi-final, the all-London affair was confirmed after Spurs edged out West Ham 2-1 in their Carabao Cup quarter-final, while Chelsea won 2-0 away to west London neighbours Brentford.
The two-legged semi-final matches will take place in the weeks of January 3 and 10, with the Carabao Cup final at Wembley Stadium on February 27.
Liverpool fought back against Leicester to win 5-4 on penalties and reach the semi-finals of the Carabao Cup in incredible fashion.
Second-choice goalkeeper Caoimhin Kelleher saved two penalties in the shoot-out as Liverpool, joint record winners in the competition with eight, reached their 18th League Cup semi.
Substitute Diogo Jota struck the winning spot-kick – having come off the bench to score – but the real hero was Takumi Minamino who made it 3-3 with seconds remaining of six added minutes.
The visitors crumbled under the pressure exerted in the second half having twice claimed a two-goal lead as Jamie Vardy scored his ninth and 10th goals in 14 appearances against the under-strength Reds.
Alex Oxlade-Chamberlain briefly made it 2-1 before a brilliant James Maddison strike restored the Foxes’ advantage.
However, the introduction of first-team reinforcements for the second half changed the dynamic as Jota and League Cup specialist Minamino, with his sixth in five appearances, forced a shoot-out.
Tottenham boosted hopes of ending a 14-year trophy drought by edging out West Ham 2-1 to make the last four.
Spurs’ last silverware came in this competition in 2008 and Steven Bergwijn combined with Pierre-Emile Hojbjerg to fire them ahead after 29 minutes.
Tottenham’s lead only lasted three minutes as Eric Dier’s poor clearance gave Nikola Vlasic possession in a dangerous area.
Vlasic’s shot fell to Jarrod Bowen whose brilliant control and drag back gave him the space to beat Dier and equalise with a low shot.
Parity lasted just two minutes, however, as Lucas Moura netted the decisive goal for Spurs from Bergwijn’s pull-back.
West Ham, who were without striker Michail Antonio following a positive Covid-19 test, pressed furiously in the closing stages.
But Spurs held firm to reach the semi-finals of this competition for the third time in four years.
Chelsea scored twice late on to beat west London neighbours Brentford 2-0.
Bees defender Pontus Jansson put through his own goal 10 minutes from time to give Chelsea the lead.
The Blues secured safe passage into their first semi-final in the competition for three years five minutes later.
Christian Pulisic was brought down by Alvaro Fernandez and substitute Jorginho tucked away the penalty with ease.
Chelsea boss Thomas Tuchel saw his selection plans disrupted by Covid-19 and injuries and gave debuts to three teenagers.
One of them, 18-year-old Harvey Vale, had the visitors’ best first-half chance but saw his header saved.
Yoane Wissa, Mathias Jensen and Rico Henry all went close for Brentford before Chelsea’s late double.