Galtier led PSG to the 2022-23 league title but failed to deliver success in the Champions League, with the French club knocked out by Bayern Munich in the round of 16.
According to ESPN sources, PSG sporting director Luis Campos informed Galtier on Tuesday that he was sacked by the club with former Bayern manager Julian Nagelsmann set to continue talks with the club.
Sources added that the club also held talks with former Spain and Barcelona coach Luis Enrique but have now made Nagelsmann their top target, with the German coach keen for Thierry Henry to join him as his assistant.
There is growing confidence that an agreement can be made for Nagelsmann and Henry to join the French champions.
Lionel Messi and Sergio Ramos will also leave the club this summer after the expiry of their contracts. Sources told ESPN in May that Neymar is also ready to leave PSG in the summer, with the club willing to let him go if they receive a suitable offer.