If all the other variables were the same - sure
In principle, of course the variables matter - if he had to stay in Barcelona unemployed and broke, or playing for Espanyol at 500k a year (I'd take it!), or condemned to the stands and thrown out of the squad. But that's not going to happen is it?
So what variables are that much better, surrounding a transfer to Manchester United, that it would offset a strong preference to stay in Barcelona?
Is the club more attractive or prestigious overall? No it isn't.
Has the manager a greater pull? Ten Hag surely has pull on de Jong but Xavi is a legend in itself, if only as a player. Probably Man United's biggest trump card though, after paying more.
Is there a better sporting perspective? Hardly. Barca are in CL, they've reinforced the team. Man United have reinforced too and are quite probably looking at a good future, but it would take a lot of optimism to anticipate Man United overtaking Barca in terms of sporting success over the course of the next contract (don't get me wrong, I'd be very optimistic about Ten Hag as a Utd fan)
Is he going to get paid more at United? Probably not really, especially seeing that Barca are supposed to pay up money from the last years in the coming years, and his wages were very high already. This is, of course, the LEVER in Utds hands: offer him more.
The club wants to get rid? Yeah they do and it's surely not a great feeling, but I doubt they tell him to his face, I doubt it's part of his relation to the manager or teammates, nor will it have consequences once he has stayed. Look at Dembélé.
The situation, as it's solidly reported, is that the transfer is agreed between the clubs but the player hasn't agreed terms with the buying club. It's honestly a strange way to go about it, and it should surely worry Utd fans whether it wouldn't be better to look at alternatives.
Especially seeing that Frenkie isn't all that in the first place.