Problem is that Real also want Mbappe and I think he is more a Real fan so he would rather go to Madrid than to Barca.
Sure he likes Real Madrid, but he was more of a Ronaldo fan. And it's not like Barca are some mid tier club, his uncle once said he used to watch Barca and Real games both.
With the chance to play with and eventually succeed Messi and wear that Barca no. 10 is no small feat. It also helps to have a lot of Frenchman around here. Offer him better wages, and I am sure he would at least think about it.
And PSG also get a ready made replacement in Dembele, and they get Coutinho to make their star player more settled. I don't see what's bad in that deal from PSG's point of view. Real Madrid will offer more cash, but then you have to overpay for players.
I am not saying it's a done deal. But instead of going through all that hassle for Neymar, I'd rather try my luck on Mbappe. Even if we fail, we can still get Neymar, who will be even more cheaper then.