Neither Lovren nor Joe Gomez are part of the travelling party for the team's current training camp in Marbella. Liverpool are next in action on Tuesday, February 19 when they host Bayern at Anfield.
Speaking about the injury issues, Klopp said the Croatia international's involvement in that encounter is questionable, per the club's official website:
"Dejan is not here and Joe [Gomez] is not here. That's never a good sign, I would say, but we will try everything to make Dejan available for Munich. It will be a tight race.
"For him, it makes sense in the moment to be in another place to do what he has to do. It wouldn't have helped if he was here, so we will try everything—that's clear."
James Pearce of the Liverpool Echo provided further details:
James Pearce @JamesPearceEcho
Bad news on Dejan Lovren. Difficult to see him being ready for Bayern now. Hasn’t played since he limped off v Wolves on Jan 7. Liverpool had initially named him in travelling squad for Marbella. Could well be Fabinho/Matip at CB next Tuesday #LFC https://t.co/RC8gng6QEd
Lovren has been absent since he hobbled off injured during the FA Cup clash with Wolverhampton Wanderers on January 7. His problem is one of a number recently suffered by the Reds at the back.
Gomez is set for a longer stint on the sidelines after it was confirmed he would need surgery on a leg fracture he picked up in December. In addition, Trent Alexander-Arnold has just recovered after a spell on the sidelines, returning to the side on Saturday as a substitute in the 3-0 win over Bournemouth.
What will be worrying for Klopp looking ahead to the match against Munich is the fact that star defender Virgil van Dijk is suspended for the fist leg at Anfield. Football writer Jack Lusby noted the team may have to field a makeshift defence as such:
Lovren may continue to divide opinion among Liverpool supporters, but he was part of the team that made it to the final of the Champions League last season, and he's experienced when it comes to these big occasions.
Although Bayern have been far from their best this season, in Robert Lewandowski they boast one of European football's best strikers. If Lovren can't recover in time for Anfield showdown that will be a big worry for Klopp.