First of all I think it is quite normal that all these rumors are now popping up like they always do, but this time are there are more things that could turn out to be some interesting coincidences. Like Xabi Alonso once played for Liverpool and now suddenly Klopp steps back despite leading the Premier League, then there are more rumors that Klopp's next job could be in Germany in some function. These rumors will now pop up on a weekly basis until we get the answers as to what's really going to happen.
Mourinho is still free, imagine one coach gets fired by a top team, then the next rumors will come up. Same for Mbappe. There will be a lot of stuff to talk about for us.

Right now have many manager still free not only Jose Mourinho but also have Antonio Conte and Jurgen Klopp will be free next season with potential become new manager for Barcelona. We can't speculated the future of free manager right now will keep retired awhile or want return to be manager next season during have many club without have manager. For Jose Mourinho, I am so excited if he returns to Premier League club than become Barcelona manager.
Jose Mourinho character is very good for Premier League manager club and he has high intention every matches, will possibility for Jose Mourinho become Liverpool manager next season or Antonio Conte will fill with position manager space in Liverpool.
Klopp isn't free next season. He said with absolute certainty that he will at least take a break and perhaps never return onto the bench as a coach, but he said without any doubt that he won't be coaching a team next season. I believe he wouldn't lie this way because otherwise he would disappoint a lot of people from Liverpool and that would be the last thing he wants to achieve.
Mourinho could be signed by then already. In his case I think if a Saudi club pays him a fortune, then he would decide to go there for a while. This would leave Conte only, but I think it is still a long way to go untl the end of the season and who knows who will get sacked by then and new positions open up. Just see how Manchester United or Chelsea is doing. I am not sure they will all keep their positions. Xavi will be gone and Barcelona looks for a coach, too.