I would guess that PSG may go for a manager change as well. I know that is not talked about a lot right now and maybe that won't happen but I think that they need a bigger name. I have always said the same thing and I will keep saying the same thing until I die, what PSG needs is Zidane. They will win the league and the cup anyway, they already win the league all the time and if they cared a bit more then they would win the cup too, that is just expected at this point.
However, if they get Zidane then they may win the UCL as well, he can build a team that would be better than the current one, even without Mbappe. Dude knows his own style and he knows attacking football, if nothing else it's guaranteed that they will have fun games to watch.
But that would be the worst timing ever if they now sign Zidane when Mbappe is about to leave the club. By the way I doubt that if Mbappe leaves the club, Zidane would not want to become the coach there. They should have tried like never before when there was still Neymar, Messi and Mbappe. But I think at the time Zidane was still a coach (or again) at Real Madrid? I am not sure about the timeline back then, but I think that was the situation. Now when Mbappe leaves PSG is not the same team anymore.
Zidane certainly doesn't want to take risks, especially since his record as a successful coach is still neat. With the depth of the current squad, Zidane is certainly considering his decision to coach PSG and I don't think that will happen. Mbappe has left at the end of the season and there are no further negotiations to be discussed with PSG.
If we talk about Messi's arrival at that time, it is clear that Zidane was still without a club and maybe that was the right time for PSG to persuade him to come. But it seems that PSG doesn't think like that or maybe PSG has made an offer but Zidane is still reluctant and doesn't want to train again before the right time. The criteria for the team that Zidane wants to coach are very high and maybe he will want to coach again if the squad he is given is as great as the one at Real Madrid when they won the champions league hat trick.