Arsenal definitely have the money.
They are also just as likely to get CL as United or as City.
They would have every chance if they went for him.
They're winning nothing anytime soon though, and are as likely as anything about to hit 5 years or so of post-wenger turmoil. Oh and they might lose Sanchez and Ozil in the summer which would leave Rom looking at playing alongside world-class players such as, er, Oxlade-Chamberlain and Coquelin.