The Danish centre-half is out of contract in the summer, and is not renewing with the Blues.
Bayern are facing a similar situation with their centre-back Niklas Sule.
The 26-year-old rejected a contract offer and is leaving in the summer on a free, per Goal.com.
Bayern are likely to turn to Christensen as a replacement.
German outlet Sport1 goes on to claim that Chelsea may even sign Sule, while Newcastle are also interested in his services.
Barcelona have also been linked with Christensen.