However, the 72-year-old - in his fourth spell as head coach at Bayern - has made clear his intention to step down at the end of the season.
Bayern reportedly put Klopp at the top of their managerial candidate shortlist in November but, according to the Daily Star, have been put off by recent developments at Anfield.
The report suggests that Liverpool's £75m purchase of Southampton defender Virgil van Dijk has been seen as a signal of intent that the Reds hierarchy is eager for Klopp to remain and lead the club back to glory.
The newspaper quotes a source as saying: "The Van Dijk transfer says Klopp is unlikely to be available – or looking to leave Liverpool – anytime soon."
Klopp has overseen 129 matches as Liverpool manager and has notched up 66 wins and 39 draws since taking the reins in October 2015.