As much as he's a world class player, comfortably the best PL signing this summer, it all came at the right time for Arsenal and I just don't think it would work at any other of England's CL clubs.
Chelsea are ridiculously well stocked there and City likewise, both have done their business and are happy with their squads. Us on the other hand - we are already struggling to fit both Rooney and Kagawa in the team, and forcing all 3 in would sacrifice the width we've always loved and make all those wingers redundant. Lingard and Januzaj look very promising and it's rare you have two players of that class in the same positions pushing into the side.
As much as, in the surface, it looks like it would've been the obvious move for him - United 'lacking creativity' against Liverpool, to anyone who watches United regularly it's obvious that both our number 10s were out, and a side containing both Rooney and Kagawa could hardly be described as lacking creativity. From our desperate last minute haggling over fees, it's quite clear that money is still an issue, and it would be difficult for Moyes to justify smashing our transfer record for a player we don't need.
Obviously he's class, one of the world's best players, but we aren't and have never been the sort of club to throw massive money at clubs when players of this ilk become available. It's definitely not a myth that we were approached regarding Ozil a week or so back, many reputable journalists agreed on that and it makes sense. I'd agree that Ozil would prioritise United over Arsenal if he had the choice but we didn't show any interest, which was the perfect opportunity for Arsenal. Cracking signing for them, but all their flaws leading into the window remain serious issues.