The Reds have been without their Croatia international centre-half since seeing him suffer a hamstring injury early on in an FA Cup outing at Wolves on January 7.
Klopp has been forced to manage a defensive injury crisis since then and remains without a number of senior stars.
Liverpool are, however, taking in a welcome break from domestic duty at present and have headed to Marbella for warm weather training ahead of a continental meeting with Bayern on February 19.
They are hoping that Lovren will make that contest at Anfield, but he has not travelled to Spain.
Klopp told the Reds’ 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.”
Liverpool also saw James Milner and Georginio Wijnaldum work away from the main group on Tuesday, while Fabinho is nursing a muscle complaint.
Klopp is not overly concerned by any of those absences, with the German coach confident that all three will be at his disposal by the time the German champions pay a visit to Merseyside.
He added: “It’s how it is after games, you have a couple of problems.
“Millie and Gini still struggle with their illnesses, so they did a bit of work in the hotel. Fabinho felt [something] a little bit; it will not be a problem, but there was no reason for him to be out today.
“Hopefully he can train tomorrow and if not then the day after that. None of them are serious, all will be fine.”
Liverpool are not in action this weekend having suffered an FA Cup defeat to Wolves in the aforementioned trip to Molineux.
They return to competitive competition against Bayern, before then facing arch-rivals Manchester United in a crucial Premier League fixture.