Redknapp's current deal expires at the end of next season and the Spurs manager is reported to have hired Wayne Rooney's agent Paul Stretford in a bid to secure a new contract after missing out on the England coaching job.
But Levy has yet to indicate he is ready to offer an extended contract to Redknapp, sparking suggestions the 65-year-old could be tempted to leave White Hart Lane if he gets a big-money offer from a Qatari club or even European champions Chelsea.
Redknapp insists there is no truth in speculation that his relationship with Levy is on the rocks, but he wants a new contract sorted out as soon as possible to avoid the prospect of unsettling key players like Luka Modric and Gareth Bale.
Croatia midfielder Modric has been linked with Manchester United and Chelsea, while Wales winger Bale is reportedly on Barcelona's wanted list.
"I've never had a problem with Daniel Levy," Redknapp told Sky Sports News.
"People keep talking about our relationship. I've never had a minute's problem with Daniel Levy in terms of falling out with him or whatever. I don't even know where that comes from.
"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.
"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."
With Spurs having failed to qualify for the Champions League after Chelsea's final win over Bayern Munich pushed the north Londoners into the Europa League, Redknapp believes there is a real possibility Modric and Bale could be lured away.
And he is convinced his contract situation could lead to an unsettled season as the players will be aware he may be leaving shortly.
"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," he said.
"It's not a case of me looking for security. What it's about is players knowing you've only got 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."
But on suggestions he could be heading to Qatar, Redknapp said: "I don't speak to anybody else -- I'm under contract at Tottenham. I keep seeing something about Qatar -- I've never even been to Qatar in my life!"
Source: AFP
Source: AFP