As we all know, one of the main reasons why Kylian Mbappe is trying to leave Paris Saint Germaine is because of his quest to win the UEFA champions league trophy and as a club with the most successful record in the competitive, I think Real Madrid has a better advantage in securing the signature of the France international more than any other club. Liverpool without doubt is a big European that's won the UEFA champions league on Five different editions but currently I think Real Madrid has a better chance of winning than Liverpool does.
That being said, I am very optimistic that Mbappe will chose Real Madrid ahead of any other European team if he should finally leave Parc des Princes this summer.
Well, Mbappe biggest wish is to be able to have UCL title considering that he is getting older and if he only stays with PSG, the chances of getting this title are very slim.
If say the most successful team in the UCL then the answer is Real Madrid, you are right and of course Real Madrid will always have the opportunity to win the UCL title every season because for La Liga itself Real Madrid can always get UCL ticket by finishing the League in the top position, either way winner or runner-up.
Real Madrid has collected at least 14 titles and of course Real Madrid has become the most successful team and certainly has a sufficient budget to be able to have player like Mbappe.
In fact, Real Madrid has been able to buy Mbappe since PSG proposed price last season but Ancelotti as coach took wise step by not sacrificing more of his budget to be able to have Mbappe and now they can get him without having to pay large amount of money to PSG.
I also know that Liverpool is one of the teams that can also win the UCL title, but Mbappe still has to prioritize Reap Madrid if he wants to have much better career.
Moreover, small difference in money is not problem for Mbappe if he really prioritizes his career and achievements.