The Germany international has been heavily linked with a move away from the club this summer, with Manchester United having previously been linked with a move for his services.
However, the World Cup winner snubbed that approach over fears that United will not be able to compete in the latter stages of the Champions League, leaving the path clear for PSG.
According to the 'Daily Mail', the player's agent Christian Nerlinger will hold talks with PSG's sporting director Antero Henrique on Thursday as the French giants look to push through a deal.
Bayern are believed to value the player at around £44m, which is thought to be well within PSG's budget, providing they can move on some of their fringe stars in the meantime.