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Hodgson told a news conference he believed the former Manchester United defender could "of course" take over the England job -- but warned that he should not rush into management.
Speaking as England prepared to face Costa Rica on Tuesday -- their final game of a World Cup that saw them knocked out with a group game still to play -- he said he believed Neville would become "a top-class football coach and top-class manager."
And he added that he saw no reason why he could not continue to combine a coaching career with the television punditry that has won him critical acclaim.
Asked about the prospect of Neville eventually becoming England boss, Hodgson said: "Of course he can be.
"But it would be wrong to start putting him under pressure to suggest he needs to get down to some work in a club side because the England manager's job is there waiting for him.
"When the job comes up again, who knows what candidates there will be?"
Saying that having a long career in football "gets harder and harder," he added: "I certainly wouldn't advise him necessarily to jump at the first opportunity to do coaching or management.
"The longer he can combine the two roles [coaching and punditry] the better. But I don't have any doubt in my mind that he will become a top-class football coach and top-class manager."
Despite the disappointment of a Brazil campaign that has been England's worst at a World Cup since 1958, Hodgson said there could be a more optimistic future.
"I've realised that, at this top level in a World Cup, it is unbelievably unforgiving," he said. "A moment of misfortune can throw everyone into a realm of despair that you didn't know was possible.
"We hope the next two, four, six years will bring some dividends. We are no longer capable of going through, but we're trying to build the confidence and use the potential of some quite talented players who have emerged on the scene.
"All we can do is hope that, when these players are reaching their best years at the age of 28 or 29, the work shows some dividends."
Time for Hodgson to call it quits?
The ESPN FC panel debate whether or not England should move on without Roy Hodgson and heap praise on a Costa Rica.
Hodgson announces starting lineup
England coach Roy Hodgson announces his starting lineup for tomorrow's match against Costa Rica.