I think he's more likely to leave than Messi, since he is not as affiliated with the club as Leo is. Barcelona basically saved and made Messi's career (paid for his medical bills and hormone treatment, gave him the opportunities to shine on the biggest stage, etc...). Barca hasn't done that for Neymar.
I could see Neymar moving to the Prem in the future for some absolutely enormous money, and United have as much of a chance as anyone else.
But the thing is, I think that we have already seen the best of Neymar in 2015. Most Barca fans laugh at this idea, but the reality is that since late-2015 Neymar has not improved in the slightest (if anything he's gone somewhat downhill). He is Brazilian and he loves to party, which is always a bad sign. And despite his incredible natural talent, I also don't think he is as obsessed with being the best as Messi or Ronaldo are.
This is just my opinion, and I'd love to be proved wrong, but I don't think that Neymar is going to improve anymore.