Negotiations over a new deal have stalled since the start of the year when the 65-year-old was linked with the then vacant England manager's job.
But the former Portsmouth, Southampton and Wesh Ham boss has insisted that his relationship with chairman Daniel Levy is not on the rocks, despite the delay in offering him a new contract.
"No, I haven't resigned, and I have no idea why it is being suggested that I have resigned," he told ESPN. "This is an outrage; an absolute liberty for people to be putting around this kind of rumour on the internet.
"It is not true, there is not a chance I will resign. Why should I?
"I have a year left on my contract."
Earlier this week Redknapp denied he had been approached by a club in Qatar after telling Tottenham to speed up negotiations to keep him at White hart Lane.
"The simple situation is, I've got a year left on my contract. It's up to Tottenham whether they want to extend that contract or not," said Redknapp, who joined the club in 2008 from Portsmouth.
"If they don't extend it and I go into my last year, it's not an easy one when players know you've only got a year left.
"It's not a case of me looking for security. What it's about is players knowing you've only got one year left on your contract and knowing that it doesn't work, basically.
"I think it's a situation of, 'well, he might not be here next year'.
"You don't let players run into the last year of their contract if you think they're any good, and you don't let managers run into the last year of their contract if you think they're any good.
"It's up to Tottenham. If they think I'm okay and I've done a decent job and deserve an extension, they'll give it to me.
"If Daniel doesn't think I'm worth it, that's up to him, that's up to the club. There's nothing I can do about it."