It's fair enough to expect CL status to attract interest in your club but Liverpool is a shithole and a half. It will still be hard to attract top foreign players to Merseyside because of where it is.
The top foreign players want to come and play/live in 1)London 2)Manchester. It's as simple as that because that's where the shops / lifestyles and foreign communities are.
A lot of the Liverpool players live near West Kirby, which is a reasonable upmarket area of the Wirral. Benitez lived there, as does Rush, Westerveld did too... quite a few.
Manchester isn't actually far from Liverpool at all (meaning where they live could be very similar), so there's not really much logic in the 'Manchester over Liverpool' argument