Howe left the Cherries by mutual consent after their relegation from the Premier League, after five years in the top flight.
But Redknapp rates Howe very highly and does not think relegation will bring down his stock, and believes other clubs will want the young coach.
"Maybe he felt he needed a break, even if they'd stayed up," he told TalkSPORT.
"I'm sure there will be plenty of clubs; I think Premier League clubs will, when the right jobs become available, put him at the top of their list.
"Anyone with any sense would look at Eddie and think: 'Hang on, here's a young guy who's 42 years of age. What a record, what a job he's done.'
"You've only got to listen to him, you know what he's about. He"s a very bright guy, very clever."