And with this game being played during the hectic festive schedule, the only thing that could make it worse for Klopp would be hearing that Paul Tierney was in charge. Note: he isn't.
In contrast to Liverpool, Leicester are having a mixed time in the Premier League so may see the domestic cups as prime targets.
They certainly have excellent recent memories of how good a day out at Wembley can be after beating Manchester City in the FA Cup final back in May.
When: Wednesday, December 22, 19.45 GMT
Best bets for Liverpool vs Leicester
Liverpool and Leicester have met twice previously in this competition, both sides scoring one win apiece.
The Reds' was way back in 1986/87 when midfielder Steve McMahon bagged a hat-trick while, in more recent times, the Foxes won 2-0 in a third-round clash in 2017/18.
Leicester, as discussed below, also triumphed in the last meeting between the pair when running out 3-1 winners in the Premier League back in February.
To reach this stage, Liverpool have won 3-0 at Norwich and 2-0 at Preston despite sending out severely weakened sides.
That suggests they still have plenty in depth although this is a step up.
Leicester, meanwhile, won 2-0 at Millwall and then came through a penalty shootout against Brighton after the pair had shared four goals at the King Power.
They come into the game after a confidence-boosting 4-0 win over Newcastle last time. Note that 'last time' was December 12 after their weekend clash was postponed.
In that sense, they'll have a freshness edge over the hosts, who gave their all in a pulsating 2-2 draw at Spurs which saw Klopp yellow-carded after failing to hide his frustration at Tierney's refereeing.
Last three meetings
Leicester 3-1 Liverpool (February 13, 2021)
But Leicester produced a superb fightback with three goals in the final 12 minutes as the visitors fell apart.
James Maddison's free-kick on 78 levelled the scores before a terrible mix-up between Alisson and debutant Ozan Kabak allowed Jamie Vardy to make it 2-1 three minutes later.
Harvey Barnes wrapped it up after 85 as the Reds crashed to their third straight Premier League defeat.
Liverpool 3-0 Leicester (November 22, 2020)
Klopp's side went joint top of the table with Spurs after nine games following a comprehensive 3-0 win at Anfield.
Leicester could have gone top themselves with victory but ran into a Reds side extending their unbeaten run in the league at home to a club-record 64 games.
Leicester 0-4 Liverpool (December 26, 2019)
Fresh from being crowned world club champions in Qatar, Liverpool produced one of the best performances of their title-winning season by thrashing Leicester at the King Power.
The Foxes were Liverpool's nearest rivals in the table going into the match but the Reds roared 13 points clear after a scintillating display.
Firmino scored after 31 and 74, James Milner slotted home a penalty on 71 and Trent Alexander-Arnold iced the cake with a brilliant fourth after 78 following a breakaway.
Past 10 meetings
Liverpool wins: 6
Leicester wins: 3
Liverpool goals: 19
Leicester goals: 14
Leicester look value to progress
Given a level playing field, Liverpool would blow Leicester away and book their place in the last four.
But, make no mistake, this is not a level playing field.
Klopp will send out a depleted side for two reasons: first, because his hand is forced by COVID absences and second, because this is not his priority so star names are likely to be rested.
Here's another stat to show why the Reds are worth taking on: Liverpool are winless in their last four home League Cup games. That's after two draws and two defeats.
One of those draws ended with them winning a shootout against Arsenal but it's pretty clear that Klopp's lack of real interest in this tournament beyond giving squad players a run manifests in some poor results.
Leicester have drawn eight of their last 10 League Cup games against fellow Premier League sides but in five of those they went on to win the resulting penalty shootout.
Put all this together and I think the bet here is Leicester to Win the Tie at 2/1.
They can do that by winning in regulation time or getting through via spot-kicks again.
Goalscorer bets for Liverpool vs Leicester
With COVID adding further unwanted confusion to possible team news, I'm struggling to find a Liverpool scorer.
Takumi Minamino would probably be the best bet at 7/4 given that he has five goals in his four appearances in this competition.
But as I think this could be Leicester's night, I'm going to pick two Foxes players who can help Rodgers sink his former team.
Liverpool were once linked with Patson Daka after the Zambian scored twice against them in a pre-season friendly in August, 2020.
Daka went to Leicester instead and has scored seven goals in 16 appearances for them this term.
He's made most of his starts in cup games and five of his strikes were netted in the Europa League.
The 23-year-old started Leicester's last Carabao Cup tie against Brighton and looks a decent price at 23/10 to find the net.
Again, this is without the benefit of team news, I'll also try the in-form James Maddison to score at 7/2.
The England man has four goals in his last six starts for Rodgers' men while he's scored twice in his last four games against Liverpool.
That includes an Anfield goal in the 2-1 defeat two seasons ago.