After seven years at the helm, Tony Pulis departed last week with chairman Peter Coates saying they were looking to take the Potters in a new direction.
Rudge has also recently left the club after 14 years with other changes likely to be made but he does not believe the owners are trying to take back control from the manager.
"They are trying to change the structure of the club to take it away from the more traditional approach to a more continental approach," he told The Sentinel.
"That means the club dictating the policy more and the manager getting on with the first team. They have decided on change and there was a need for change in terms of some aspects of recruitment; Tony had been dictating the terms on that.
"The manager in the past had control over players' contracts etc, but that's changing more to owners and chief executives.
"But I still cannot see Peter and John Coates overriding the manager on new signings. I don't think they would interfere that much.
"I cannot see a situation where any manager coming into Stoke says he doesn't want a player, but they go ahead and sign him any way.
"I can see a situation where the next manager will be in close association with Peter and John, but he would have the final say. I'm sure they would want it to be that way too. But in general, they are definitely taking more responsibilities off the manager."
Former Blackburn, Manchester City, Fulham and QPR manager Mark Hughes is the current favourite for the Stoke vacancy.
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