Redknapp has a year left to run on his current deal and has recently voiced his concern that he has not been able to pen a longer-term contract.
Reports on Wednesday claim Redknapp will meet Levy to discuss whether he still has the full backing of the Spurs hierarchy.
Redknapp guided Spurs to fourth in the Premier League last term, but was unable to secure Champions League football due to Chelsea's victory over Bayern Munich in the European Cup final last month.
Although a top-four finish was the goal at the start of the season, many Spurs fans were unhappy with the way Tottenham threw away a 10-point lead over Arsenal to end the season in fourth rather than third.
Indeed, Tottenham were primed for a title push thanks to an excellent 11-match unbeaten run towards the end of 2011, and even had a chance to move top of the table in January.
Redknapp claimed his team were capable of ending Spurs' 51-year wait for the title, but a poor run of one win in seven league matches in the latter stages of the season cost the north London club a place in the Champions League.
That run coincided with speculation that Redknapp would replace Fabio Capello as England manager after the Italian resigned in February.
Many were angered Redknapp publicly flirted with the idea of becoming Three Lions boss, but the 65-year-old insisted it had nothing to do with his team's poor run, which was followed by a humiliating 5-1 defeat to Chelsea in the FA Cup semi-final at Wembley.
On Tuesday, Redknapp angrily denied rumours he had resigned, telling ESPN: "No, I haven't resigned, and I have no idea why it is being suggested that I have resigned.
"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 suggestions he was being courted 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," he said. "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."