A win over the Cottagers by any margin will give the Reds their biggest goal difference (currently +16) and equal their highest points tally (30) ever in a Premier League campaign after 12 games.
And should Klopp's side keep a clean sheet against bottom-side Fulham, they will become the first LFC team ever to have conceded as few as five goals at this stage of a Premier League season.
For more need-to-know pre-match facts and figures, courtesy of club statistician Ged Rea, read on...
Overall in the Premier League Liverpool have won 16, drawn four and lost six of the 26 meetings with Fulham.
At Anfield, the Reds have won eight, with four draws and one defeat.
The clubs last met in the 2013-14 season when Liverpool completed their second successive league double over the Cottagers.
Liverpool have kept nine clean sheets in the last 16 meetings with west London club home and away.
Daniel Sturridge's only hat-trick for Liverpool came against Fulham at Craven Cottage in May 2013.
Sturridge, Steven Gerrard and Luis Suarez have scored the most against the Londoners for Liverpool in the Premier League era. All have netted four times.
Only against Aston Villa and Newcastle has Sturridge bagged more goals for the club - scoring five times.
Eleven goals have been scored by Liverpool substitutes against Fulham. Only Stoke (13) have conceded more to players coming off the bench for the Reds.
Sadio Mane has scored for Liverpool in 19 Anfield games in all competitions. The Reds have won them all.
The Cottagers have won once at Anfield in 33 visits in all competitions - in May 2012 while Martin Jol was manager.
In the victor’s line-up that day were former Reds John Arne Riise and Danny Murphy, plus ex-LFC youngster Alex Kacaniklic.
Fulham's former Chelsea winger Andre Schurrle has scored 11 of his 15 career Premier League goals away from home - a ratio of 73 per cent.