Redknapp, who has steered Tottenham to their best start in the Premier League with five wins from seven games, was made even-money to leave after being 50-1 a day earlier.
Bookmakers were puzzled by the rush of bets on Redknapp but he dismissed suggestions he was about to quit.
"I'm definitely not leaving. It's absolute nonsense. I couldn't be happier. I love it here and I have no intention of leaving," Redknapp told reporters before setting off with the team for Saturday's game at Bolton Wanderers.
A spokesman for bookmakers William Hill said the rush of money on Redknapp had probably been due to a "bandwagon" effect with rumours spreading across Internet chat rooms.
"The rumour mill has been in overdrive with all sorts of unlikely scenarios being offered up by punters wanting to bet that Harry will be the first boss out," said spokesman Graham Sharpe.
"We don't necessarily believe any of them but we can't afford to take a chance so have to keep cutting the odds as the demand continues."
Redknapp left Portsmouth 12 months ago to replace Juande Ramos at Tottenham and steered the London club away from the relegation zone. They are now fourth in the table.
