It could happen, but as you say, it doesn't make sense because Barcelona are struggling financially. And also for now their squad seems better prepared with the presence of new players, especially Gundogan who was brought in for free from Manchester City.
I have a ridiculous thought about Barcelona and Mbappe, I mean Mbappe will end his contract next season, that means there will be a free transfer, well I want to see if they will be one of the teams that will compete for Mbappe or not with his free agent status. Lol, that was my wild thought.
It is obvious that Barcelona would have to sell half of the club to get him lol, there is no possible way they could ever get him, hell it's a miracle they are keeping their own players, let alone even think about Mbappe. Real and City are the only other two teams that has enough money to spend, another was PSG but that's already his club anyway.
So if Mbappe leaves, which I still think he won't and this is all a ruse to get a lot of money from PSG, then I guess that it's going to end up with something much bigger pay from PSG. I am sure that if he goes to Real though, he will be regarded as one of the best of his generation and he could win a ton of cups and a lot of leagues and probably a lot of UCL until he retires as well.
They haven't even been able to stabilize their current cash book even though they have issued Busquets

Barcelona is still in a situation that is still a bit complicated right now so this is indeed possible but there are many considerations including conditions that really require them to make big steps by selling some players lol
Talking about Mbappe, now indirectly with that big price, everything returns to Madrid, it's just that this condition won't be easy, but indeed if Mbappe and PSG's cold war continues then something like this will definitely happen sooner or later.