According to what I understood from Galtier's words in his interview he said that he wants to stay for another season in PSG. Galtier is a good coach but not for a team like PSG, a team like PSG needs someone with better experience to manage the superstars they have otherwise there will be more selfish players like Mbappe or Messi and a more negative atmosphere in the team. I think the best they can do is to replace Galtier with another coach for the next season because of the bad results they got.
Yes, some media reports, that Galtier said he deserves a second season at Paris Saint-Germain amidst the rumors going out. As quoted by Goal, Christophe Galtier believes he deserves one more chance to prove his credentials after delivering the Ligue 1 title to Paris Saint-Germain. In fact, we don't know what Galtier's problem is with PSG. IMO, Galtier doesn't have full power in the locker room, plus he doesn't have the capacity to bring in the players he wants. in the end, he didn't have much choice.
From my point of view, Galtier is a coach who has quite a lot of strategies. Unfortunately, he didn't get the formation that became his flagship standard. maybe, something is a problem for him. or, the available players are not ideal for the system he wants, apart from Trio MNM.
By the way, as reported by Dailymail, currently PSG is considering Luis Enrique to replace Galtier as their new manager. however, if it's management that always chooses the player they want. I think, whoever the coach is, the results will not be much different from other trainers.