According to MailOnline's Sami Mokbel, the currently unattached Klopp wants to know whether he stands a chance of succeeding Pep Guardiola at Bayern before he commits elsewhere.
Guardiola's three-year contract at the Allianz Arena runs out at the end of the season, and should it not be renewed, Klopp would surely be in the running to take over after his success in seven years with Dortmund.
Klopp left the managerial role at Dortmund at the end of the 2014-15 season. Almost as soon as he announced his imminent departure from the Westfalenstadion, he was being linked with a switch to the Premier League, specifically Liverpool, per MailOnline's Martha Kelner.
He is seen by many as a perfect fit for Liverpool, a club where the fans and the team's traditions play important roles, per football writer Tancredi Palmeri:
According to Chris Bascombe in the Telegraph, current Reds manager Brendan Rodgers has come under pressure of late following a poor sixth-place Premier League finish last season and a mediocre start to the 2015-16 campaign.
It is unsurprising that the 48-year-old is being so widely touted for the Liverpool managerial job.
Despite a disappointing final season with Dortmund, he was largely a huge success there and won two Bundesliga titles despite the fierce competition from financial heavyweights Bayern.
A manager who can build a title-winning team is exactly what Liverpool have been crying out for since they last triumphed in the English top flight in 1990.
Klopp looks like the obvious choice to replace Rodgers should the Northern Irishman continue to return poor results.
However, it seems that should Bayern want Klopp to be Guardiola's successor, the German will opt to return to the Bundesliga rather than make a move to England.