It is understood the Bundesliga outfit have contacted Markovic's representatives to discuss the possibility of signing the former Benfica man, but reports suggest those discussions are at an informal stage.
Markovic, 22, was a £20m signing in 2014 under former boss Brendan Rodgers, but despite the hefty price tag, he was sent out on loan to Fenerbahce last season.
The 22-year-old has already rejected Sporting Lisbon's advances after the Portuguese side were unable to finance the fees involved.
Klopp has already made himself clear that players on the periphery of the Liverpool squad should be actively seeking for a way out of Anfield.
The former Borussia Dortmund boss said:
"When there's no chance to play, it makes absolutely no sense.
"We have a few players, maybe, who want to leave us and I'm pretty sure that will happen. And one or two more players will join us from other clubs.
"It's a long time until the 31st of August and we have to work a little bit."