The Reds are currently top of the Premier League after 17 games, winning 14 of them and drawing just three.
Jurgen Klopp’s side have conceded just seven goals as they sit one point ahead of reigning champions Manchester City.
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City have tasted defeat this season, recently beaten 2-0 by Chelsea.
Liverpool travel to the Etihad to play their title rivals on January 3 with a number of festive fixtures between now and then.
Arsenal are the only team to ever go through a Premier League season without losing a game, waltzing to the title in 2004.
And Lovren has revealed Liverpool now aim to copy that Invincibles side.
“Hopefully we can be unbeaten until the end of the season,” Lovren said.
“Of course it will be a challenge but this is what we want, this is why we came here to Liverpool, because we know we can do it.
“Arsenal did it before so why not?”
“There are so many games in front of us and in front of them [Man City].
“It will be a tight race and it’s not only City. Tottenham is only a couple of points behind.
“You cannot sit and enjoy and say: ‘We have five or six points in front of everyone’.
“It doesn’t work like that. Every game for us is a final.”
Liverpool travel to Wolves on Friday (8pm) and star defender Virgil van Dijk has sent a warning to his own team ahead of the clash.
“We are in mid-December and the season is still too long,” said Van Dijk.
“We are very happy we’re in the position that we’re in now but that can change in two or three weeks so we won’t get carried away.
“We’ll try to keep on doing what we’re doing and, obviously, stay confident.
“It (Wolves) is another game we want to win. It’s going to be very tough there.
“They are in a great moment but so are we so we will have to prepare well and know their strengths and their weaknesses as well.”