The reds travel to Molineux, hoping to build on a fantastic set of results since the end of the international break.
Liverpool have won all four of their fixtures, and quite comprehensively too but must now face Diogo Jota's old club at their stadium.
Wolves have found it difficult to score but have opposing teams have found it equally difficult to score against them this season. It will be interesting to see if the reds can sustain their recent free-scoring nature.
They have scored four goals in each of the last three Premier League games - against Arsenal, Southampton and Everton - all three games on Merseyside.
Klopp's side start the weekend just two points away from the top. Chelsea have already been beaten this weekend - Liverpool can go top with a victory.
Follow the game with us here.
As it happened...
No changes to the starting line up from the 4-1 win over Everton.
Alisson, Alexander-Arnold, van Dijk, Matip, Robertson, Fabinho, Henderson, Alcantara, Salah, Mane, Jota
Subs: Kelleher, Konaté, Milner, Oxlade-Chamberlain, Minamino, Tsimikas, Origi, Williams, Phillips
And here's how the home side look for today's game.
Sá, Coady, Kilman, Saïss, Aït-Nouri, Neves, Semedo, Dendoncker, Jiménez, Hee-Chan, Traore
Subs: Ruddy, Hoever, Podence, Moutinho, Silva, Trincão, Campbell, Bueno, Cundle
How incredibly strange of their fans?
3' Some early opportunities from Liverpool. Looking dangerous but some final balls a bit off target.
6' The sixth minute marks a moment of applause from around the stadium in memory of six year old Arthur Labinjo-Hughes.
Travelling Liverpool fans end the applause with a rendition of You'll Never Walk Alone.
15' It's some way offside but Jiminez collects the pass from Hee-Chan.
He blazes it over the bar before the assistant raises his flag.
17' Couple of corners for the reds. Swung in by Trent Alexander-Arnold and Jota gets a header but it's straight at the legs of a defender.
19' Good defending required from Wolves in the area. Trent had played in Jota but he was succesfully crowded out.
28' Liverpool keep up the pressure and it ends with Thiago flicking the ball over the defenders head and into the path of Trent.
He hits it first time in the air and it goes over the bar. Best chance of the game for the reds. 0-0.
32' Trent whips it in.... Jota rises highest and heads... narrowly wide.
Pressure starting to build...
35' Adama Traore is a handful.
He outmuscles Thiago in the middle of the pitch and lofts a ball forward to Jimenez. Alisson is alert to the danger and collects.
38' Jota finds Robertson who plays the ball across the face of the goal.
You think Salah is going to stick that into the net but it's a remarkable tackle from Romain Saiss.
Easy to see why they have such a decent defensive record.
41' Lengthy stoppage for Conor Coady. But he's back on his feet and on the pitch now. There will likely be a few extra minutes added to this half.
45+1' Ait-Nouri sends in a low pass into the area - it's aiming at Traore but Alisson is there to spread himself wide and Robertson helps clear the ball.
First major moment of panic in the reds defence.
Wolves 0-0 Liverpool
The reds have had the better of the chances but Wolves defending has been excellent. Lots of work for the reds to do in the second half.
A late chance for Wolves proved that they too will fancy taking all three points here.
No changes in personnel at half time.
Can either side get the win here?
57' It's a little bit 'pinball' at times now. The reds had a threatening corner which Thiago drilled around the penalty box.
Crowd getting a little livelier but still no breakthrough for the reds.
A short backpass requires Alisson to come out of his area and slide to kick that ball back to van Dijk.
60' Mix up at the back from Wolves, Jota is in, the keeper is stranded.
He powers towards goal and absolutely smashes that shot from six yards but straight at the retreating Conor Coady.
No doubt about that - it should be 1-0 to the reds.
62' Fabinho booked for a foul on Adama Traore.
Still catching breath from that Diogo Jota chance.
63' Romain Saiss free inside the area. Hits it over from the cross.
But he was offside. Explains how he was in so much space.
65' Andy Robertson now into the referee's book. Another tackle on Traore.
67' The reds make their first change.
Henderson off and Origi on. Klopp wants to go for it here.
70' Mane and Salah play a one two. Mane judged to have caught the keeper with his foot - the Wolves keeper Jose Sa wins the free kick.
74' Mane and Jiminez race for a ball by the Liverpool goalline. Jimenez ends up sliding towards the advertising hoarding.
He then heads back to the pitch before sitting down and awaiting treatment. Not very sporting.
79' Joao Moutinho is on to replace Hwang Hee-Chan.
Trent lets rip with a shot but it's over the bar.
81' Oxlade-Chamberlain comes on for Diogo Jota.
In to the final ten minutes.
It remains 0-0.
87' Mane inside the area and lands the shot but Jose Sa saves it.
88' Trincao replaces Traore with a couple of minutes remaining.
90' Salah with a turn and swipe at the ball but the keeper is there again to stop it.
Five minutes of added time.
THE NINETY FIFTH MINUTE!!!
DIVOCK ORIGI SCORES!!!!!!!!!!
Salah passes, short to Origi, spins and smashes it through the legs of the keeper.
Wolves 0-1 Liverpool (Origi 90+5')
Liverpool were the better side. Wolves were incredible in defence.
But after Jota missed a gilt edged chance, up stepped substitute Divock Origi to score a very very late winner.
The kind of late winner that could spurn a title winning season.
The reds go top of the league, at least until Man City take on Watford tonight.
Man City do play later this evening, but Liverpool have turned a 4 point deficit to Chelsea to a one point advantage inside two weeks.
Five fantastic wins since the international break.