BILD says Reds boss Brendan Rodgers is an admirer of Boateng, who spent a season at Manchester City before leaving for Bayern in July 2011.
Manchester United manager David Moyes is also interested.
Boateng extended his contract at Bayern until 2018 last December, when he revealed his happiness in Munich.
"I am happy," Boateng said. "FC Bayern are one of the biggest clubs in world football. I want to achieve more success here."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball