Schneiderlin would get into City, United and Arsenal's midfield and they should all be looking at him as an option. I'd even go as far as saying he'd get in Chelsea's lineup - if they moved Fabregas forward. I think Chelsea and City will both be looking for a bigger name, but unless Arsenal and United do the same then I can't see them missing their chance on a player like Morgan. Still, let's hope Arsenal stick with Coquelin with Ramsey, Cazorla and Wilshere capable of playing there, and United try and go for someone like Pogba.
City don't always go for big names, weirdly enough. Obviously they mainly do, but players like Fernandinho weren't exactly household names or even recognised full internationals. Homegrown is almost certainly more important at the moment.