Arsenal have a great fan base, they have suffered for years, IF the owners invested which I believe they now realise they have to do, Arsenal have the potential to be a major force.I'm not sure that Arsenal is a great job. Not a great fan base with the stadium being half empty for lots of games and ownership who are more interested in the money than actually winning anything. At Leicester he is privy to the inner circle and part of the decision making process, maybe a big fish in a little pond but it will look good on his CV. The inevitable failure at Arsenal would hamper his ambitions greatly.
The only jobs suitable for Rodgers in England are us or Arsenal.