The Reds remain on course for a first league title since 1990, but they know that any slip-up against 14th-placed Palace would allow champions Manchester City the chance to close the gap.
The Reds once again play before City this weekend and so would open up a seven-point lead at the top of the table with victory, although anything less would not only allow the champions to close the gap on Sunday, but also pile more pressure on the shoulders of Liverpool.
Klopp's side so far appear unfazed by such pressure, though, and they produced a gritty 1-0 win over Brighton & Hove Albion last weekend to bounce back from successive defeats, including their first league loss of the season at Man City.
January has been a traditionally poor month for the Reds under Klopp - they have lost more games than they have won in the month during his tenure - but this Liverpool team is beginning to make a habit of bucking previous trends and have showcased the crucial title-winning quality of picking up wins even when not playing particularly well.
Saturday marks their first home game of 2019 too, and the Reds are currently on a 31-game unbeaten run at Anfield in the top flight - their joint-second longest ever run after the club-record streak of 63 between February 1978 and December 1980.
Crystal Palace were the last visiting team to win a league game at Anfield incidentally, but Klopp's side should be confident of avoiding that fate this weekend having won each of their last six outings in front of their own fans. Another victory in this match would see them make it seven on the bounce for the first time since January 2014.
Perhaps even more impressively, Liverpool have conceded just three goals in their last 15 Premier League home games, and they boast by far the best defensive home record in the Premier League this season.
Indeed, home and away only one team in English top-flight history has ever conceded fewer goals at this stage of a season, and it is that defensive record which has provided the foundation for what looks like Liverpool's best chance of winning the title since 1990.
Such are the standards in the Premier League nowadays that a four-point lead can be wiped out very quickly should Liverpool hit a blip, but victory on Saturday would take them another small step closer to ending their drought.
Recent Premier League form: WWWWLW
Recent form (all competitions): WWWLLW
There will not be too many people expecting Palace to get much out of their trip to Anfield, but the same was true just before Christmas when Andros Townsend's rocket helped fire them to a shock win at the Etihad Stadium.
Roy Hodgson did his former club a huge favour on that day, but the Palace boss will not be so generous this weekend as he returns to the ground where he spent a brief and unsuccessful spell in 2010-11.
Hodgson won just seven of his 20 league games in charge of the Reds, but he is unbeaten in four trips back to Anfield as a visiting manager since and has seen his side keep clean sheets in all of those games.
It would be a major surprise if he is able to extend that record on Saturday, although Palace have kept more clean sheets than any other team outside the top four this season, while only Leicester City have conceded fewer goals outside the Champions League places.
On the flip side, Hodgson's side have also only scored one goal on his four previous returns to Anfield, and Palace as a club have failed to score in six of their past seven league games against teams beginning the day top of the table.
The Eagles' form of late has been patchy, following up their win over Man City with a goalless draw against Cardiff City and then falling to a 2-1 defeat to Watford last time out off the back of an impressive victory at Wolverhampton Wanderers.
Palace have won three of their last six league outings, though - as many as they managed in their opening 16 of the season - and have not suffered back-to-back defeats in more than a month.
Hodgson's side have been particularly impressive on the road too, picking up more points away from home than they have at Selhurst Park in addition to scoring more than twice as many goals on their travels.
Indeed, their last two away outings have seen them win at Man City and Wolves, and should they add Liverpool to that list then it would equal the club's top-flight record of three successive away victories.
Palace boast a decent record at Anfield too, and it could be that the Eagles have another telling say on the title race this week.
Recent Premier League form: WWDLWL
Recent form (all competitions): WDLWWL
Liverpool could welcome Joel Matip back into their starting lineup after the centre-back was named as an unused sub against Brighton last time out.
James Milner could fill in as an emergency right-back to cover for the youngster, but Fabinho is able to move back into his favoured midfield position despite impressing as a makeshift centre-back last weekend.
Georginio Wijnaldum will undergo a late fitness test to determine whether he can start after a knee problem of his own.
Thirty-nine-year-old Julian Speroni is therefore in line for his first appearance in more than a year, while former Liverpool striker Christian Benteke could make his first start since September after returning from injury off the bench last weekend.
Liverpool possible starting lineup:
Alisson; Milner, Matip, Van Dijk, Robertson; Fabinho, Wijnaldum; Shaqiri, Firmino, Mane; Salah
Crystal Palace possible starting lineup:
Speroni; Wan-Bissaka, Tomkins, Sakho, Van Aanholt; Kouyate, Milivojevic, McArthur; Townsend, Benteke, Zaha
Head To Head
However, Palace do have an impressive record at Anfield, winning three of their last four league games away to Liverpool.
The exception in that run came on their most recent visit, though, when Mane netted once again to give Liverpool all three points in the corresponding fixture last season.
We say: Liverpool 2-0 Crystal Palace
Liverpool have offered no signs that their recent defeat to City will derail their season, and their home record will make them huge favourites to pick up another win this weekend. We cannot see Crystal Palace getting anything from the game.