If Mbappe stays with PSG this season, and leaves PSG as a free agent next season, there are many clubs who would like to have Mbappe in the squad. And they will offer Mbappe big bonuses and high wages. Real Madrid and Bayern Munich are among them. Chelsea and Liverpool will also try to sign Mbappe. Even this season, these two clubs have tried to bring Mbappe into the team. I also think Newcastle will also want to strengthen their squad next season. As they are very rich club. So they can offer Mbappe a big offer to bring a big star player like Mbappe into the team next season.
I think Mbappe would want to play for at least one year on loan at Chelsea where he should mature enough as a player to go to the bigger teams of PSG,Real,Bayern or Liverpool.I am always against moving up the ladder to fast no matter how good of a player you are when you are still young and you need to play in a team of average/good level gaining some beneficial experience before moving up to a top team.
Newcastle would be a good option also for him as they are in the same league as Chelsea but with them he would be playing in Champions League so not missing anything,both are good options which I think he should consider.
It would be good for Mbappe to play 1 year in any Premier League league. Liverpool is a strong team. They have a strong squad. If Mbappe is with this team, he will become more experienced. Also able to score a lot of goals. Because almost all the players in the squad are very talented.
I find Liverpool a better team than Chelsea and Newcastle. The performance of the Chelsea team was terrible last season. On the other hand Newcastle team played very well last season. However, this team lacks stars and experienced players. It would be foolish for Mbappe to join Newcastle for just 1 year. If Mbappe wants to go on loan for 1 year, Liverpool would be the most perfect team.