Redknapp has been loosely linked with other jobs after an encouraging start to the Premier League campaign with Pompey, but Smith has moved to rubbish such speculation.
"I'm not surprised Harry has been linked with a move. He's done a tremendous job and proved what a quality manager he really is," Smith told the Portsmouth News .
"He's one of the best around, no doubt about it, so he's bound to be linked with other clubs. It's only to be expected.
"I wouldn't have thought he would leave, though. He enjoys it at Portsmouth. It's a club close to his heart," he added.
"I can't see him ending all that and going anywhere else. I don't think there's any need to worry."