The Reds are battling on both fronts, flying high at the top of the Premier League with one foot in the last-four in Europe.
They travel to Porto on Wednesday for the second leg of their Champions League quarter-final already 2-0 up in the tie.
But many Liverpool fans would happily be knocked out of the competition if it meant a first ever Premier League title was won this season.
The Anfield outfit have never won the competition since it was rebranded in 1992 with the last league title coming in 1990.
And former Liverpool goalkeeper David James believes Klopp needs to keep focusing on winning each and every game.
“Liverpool fans are saying they’d rather win this than that, but they can because they don’t have to go out onto the pitch,” James said.
“If Jurgen Klopp ever gave the influence that one game was more important than the other, then it undermines the whole ethos.
“They win against Chelsea, then they have to go to Porto, they have to win against Porto.
“They’ve got five more league games which they have to win and then the semi-final which they have to win.”
Liverpool moved back to the top of the Premier League on Sunday thanks to a 2-0 win over Chelsea.
Sadio Mane and Mohamed Salah netted the crucial goals which sent the Reds back to the summit after Manchester City had temporarily moved ahead.
And Salah knows Liverpool can’t give up, even though City still have a game in hand.
”In my opinion, yes,” Salah replied when asked by Sky Sports if four wins would be enough for Liverpool to win the title.
“We just need to focus on our game and hope Manchester City will lose points.
“I did follow Man City to see the result, it can help us but also it can push us to perform better.
“You need to score, you can’t lose any points, I knew the result of Manchester City’s game.”