I think it should be another coach. The first name that comes to mind for me is Jose Mourinho...
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PSG sacked Galtier in the end of the season and he wasn't the only one leaving the club that way lately. Maybe this was the reason why Mourinho didn't want to move to Paris. I read that they failed to find an agreement with Nagelsmann too but it seems that Luis Enrique is the closest coach to sign contract with them as soon as this week from what I read in media.
Galtier failed to stabilize the PSG team. And we were sure that PSG will not keep Galtier as coach next season. PSG needed an experienced coach like Zidane. But Zidane is not interested in coaching PSG. On the other hand, I haven't heard any rumors about PSG wanting to coach Nagelsmann. However, in recent times, it seems that Luis Enrique will be the coach of PSG management. I think PSG will be stronger if they get an experienced coach like Luis Enrique. However, Luis Enrique must be allowed to operate freely. PSG's performance will not stabilize if Luis Enrique is unable to operate independently.