If Mbappe's goal is to win the Champions League, it is natural that he will move to a club that has a greater chance of winning, such as Manc City, Real Madrid, Munich or Barcelona.
However, the one who really needs a pure striker right now is Real Madrid. And we know Real Madrid is the defending champion for the Champions League. He has a big chance if he joins there to win the championship.
How many times have he and PSG been defeated by these clubs in the preliminary round. I have to be honest, PSG's chances of winning the Champions League are still very far away compared to the clubs I mentioned earlier.
I think only Real Madrid, Man City, and Bayern Munich that have bigger chance to win UCL title. I'm sorry I exclude Barcelona because it seems hard for Barcelona to win UCL title with their current condition. Mbappe should move to those 2 teams/clubs if he wants to have a good chance to win UCL title in the future. However, I think Real Madrid is still the best team in UCL which already wins more titles over other teams. Real Madrid also has a great coach and potential players to be stronger clubs in the future.
PSG will be always difficult to win UCL title because they have no proper mentality to win it. PSG has no player who can influence other players to play consistently during the match. It is the role of the captain team or the senior players who have a lot of experienced in the competition.
Those teams you were mentioned above indeed strong teams and traditionally they always being an champion candidates for every season especially Manchester City although their performance a bit decline but their performance since group stages is still stable and for Real Madrid too in the last 10 years this team can able to being an the champion 5 times so obviously they cannot be underestimate and for Bayern Munich i was interested to see how far they will go in this competition because they have impressive performance at Champion league and Bundesliga with Harry Kane as their main striker
Barcelona under Xavi still lack of experience in Champion league even last season Barcelona has showing poor performance and finish at 3rd place of group stages and when playing at Europa League too Barcelona was eliminated by Frankfurt on knockout stages so Barcelona under Xavi is still cannot considered as strong candidate of champion league and this season too Barcelona even have to lose from weak team Antwerp in the last match of group stages so their performance cannot be says impressive