James is now into the second season of a two-year loan at Bayern from Real Madrid and the Germans have a permanent option available to trigger.
Bayern are keen to hold onto the Colombia international, but only if James is committed to the club long-term.
A source told Kicker: "There are doubts within the club about whether James himself wants to continue playing for Bayern."
James is yet to start a game for Bayern under new coach Niko Kovac - which has seen him raise concerns within his circle.
Should Bayern fail to be convinced of the midfielder's commitment, they're prepared to send him back to Real where he has a contract to 2021.