The Black Cats remain in the relegation zone, four points from safety, while Liverpool's Champions League hopes are drifting further and further away, with 11 points now the gap to the top four.
With just 14 games of the season remaining, Liverpool now face an uphill battle if they are to haul themselves back into the reckoning for a Champions League place.
All of those currently occupying the top four also find themselves in contention for the Premier League title, and while Liverpool's name has been whispered in the same breath at various points of the campaign, right now such heights seem as far away as ever.
Jamie Vardy once again stole the headlines for the Foxes, scoring both goals including a stunning opener, but from Liverpool's point of view it was another toothless and uninspiring display.
Kasper Schmeichel was barely tested in the Leicester goal as Liverpool made it three consecutive games without scoring since netting five times against Norwich City.
Why Liverpool can look so dangerous in attack some weeks and so devoid of ideas in others appears to remain a mystery to Klopp, but it is one that he will need to solve soon if the Reds are to salvage anything from their season.
February looks like being just as busy as January was, and it is likely to be a pivotal month for Liverpool one way or the other. West Ham United await in an FA Cup replay on Tuesday, while Liverpool are also in Europa League action before finishing off the month with the League Cup final against Manchester City.
There are plenty of competitions to juggle, then, and the Premier League is in danger of dropping down the list of priorities should their inconsistent form continue. Liverpool have actually averaged fewer points per game under Klopp than they did under Brendan Rodgers in the league this season.
They have won just one of their five league games so far in 2016, and that came in the dying minutes against struggling Norwich, so it is imperative that they improve their form in back-to-back matches against Sunderland and Aston Villa.
Recent form: WLDLWL
Recent form (all competitions): LWWLDL
As frustrated as Liverpool fans may be with their team's current form, they won't receive much sympathy from the Sunderland faithful.
The Black Cats once again find themselves embroiled in a relegation battle, with four points currently separating them from Norwich in the sanctuary of 17th place.
Sam Allardyce did business in January in an attempt to improve his side's position, but the concern will be that the teams around them in the table - with the exception of Aston Villa - splashed even more cash than he did.
Of course, money does not always translate to success on the field, and Allardyce will be hoping that the arrivals of Lamine Kone and Jan Kirchhoff are exactly what Sunderland need to shore up their defence - the weakest part of their side and the weakest back four in the league, according to goals conceded.
In addition to that defensive duo, Wahbi Khazri and Dame N'Doye also joined, and all four were involved on Tuesday night as Sunderland put in a valiant - if ultimately unsuccessful - showing against Manchester City.
While the performance may raise belief, the fixture schedule certainly doesn't make kind reading for Sunderland fans right now. Following on from Man City and this weekend's visit to Liverpool, Sunderland face Manchester United, West Ham, Crystal Palace, Southampton and Everton in their next five games.
Considering they have not beaten a team outside the bottom five since November, that could effectively be a relegation-sealing run of fixtures for Allardyce's side.
The Black Cats will arrive at Anfield this weekend having lost 10 of their 13 away matches in all competitions this season, while in the Premier League alone they have conceded a league-high 34 goals and amassed just seven points on the road - only Villa have managed fewer.
However, they have at least scored in their last seven Premier League away games, which is their best run since April 2013, and with Liverpool misfiring at the moment, Allardyce will feel that his side have a fighting chance this weekend.
Recent form: LWWLDL
Recent form (all competitions): WLWLDL
Klopp is close to a substantial fitness boost, with a number of first-team players on the verge of returning to training, but this weekend will come too soon for them.
Klopp must also decide whether to stick with Roberto Firmino, who has four goals in his last four Premier League games, or switch back to Christian Benteke, who has six goals in seven Premier League appearances against Sunderland and scored the only goal when they met in December.
Khazri could make his full debut regardless of the results of those tests, although Allardyce is unlikely to make too many changes to the side that ran City close.
Liverpool possible starting lineup:
Mignolet; Clyne, Lovren, Sakho, Moreno; Can, Lucas, Henderson; Milner, Firmino, Lallana
Sunderland possible starting lineup:
Mannone; Jones, Kone, O'Shea, Van Aanholt; Khazri, M'Vila, Kirchhoff, Cattermole, Borini; Defoe
Head To Head
Liverpool are unbeaten in their last seven matches against Sunderland, winning five of those. The Black Cats' last victory over the Reds came in March 2012 when Nicklas Bendtner scored the only goal of the game at the Stadium of Light.
You have to go back to 1983 for Sunderland's last victory at Anfield, when a Liverpool side including the likes of Alan Hansen, Graeme Souness, Kenny Dalglish and Ian Rush were beaten 1-0 on Merseyside.
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We say: Liverpool 1-0 Sunderland
Sunderland were much better against Man City last time out, but they will go into this match as heavy underdogs once again. Liverpool meanwhile, have been nowhere near their best in recent games but should still have enough to see off their struggling visitors.