With Joe Gomez injured and Virgil van Dijk suspended for the last-16 first-leg tie at Anfield , having Lovren available would be a major boost for the Reds.
But Klopp told Liverpool's official website it is too soon to make a decision.
"I don't know 100 per cent. It's Monday and we play on Tuesday so most of that should be clear," he said.
"Dejan, I actually have to wait minute by minute if there is a chance or not."
Klopp sounded more hopeful on the availability of former Bayern winger Xherdan Shaqiri, who has been contending with an abdominal problem, and Georginio Wijnaldum following his recovery from illness, with the pair having taken part in training.
"Gini trained and looked really well. Shaq did a lot, so it will be close, we have to see," he added.
With Lovren's status still uncertain, Fabinho could be utilised as at centre-back but Klopp says the onus will be on the whole team to put in a shift defensively.
"In the Champions League, against Bayern Munich, it's not an easy job. It depends on how we defend in general," he added at a news conference.
"There will be a lot of moments when we have to defend, and we've worked on that.
"We respect the qualities of Bayern Munich a lot: speed, technique, experience. We try to make the best of the situation."