It had been thought Spurs would definitely push through with the £450million redevelopment of their current ground if they were unable to convince the Olympic Park Legacy Company to back their proposed £250million move to Stratford.
But Levy has now branded the so-called Northumberland Development Project currently "not viable", and when asked if the club's next home might be outside Tottenham even if the Stratford strategy did not succeed, Levy told Sky Sports News: "Correct. The problem with the situation we're in now at White Hart Lane is that the project currently is not viable."
He added: "So we would have to go back to the drawing board and that would obviously mean looking at other locations again.
"It's one of those emotive items that, if one had a choice, we would rather be building here, we would rather have fantastic transportation links.
"But what is clear for this club is that in order to compete at the highest level within the Premier League and European football, we need to solve the stadium (issue).
"We need a larger stadium, and if that means we have to move out of the area, I think the fans will back us."
Some Spurs supporters have staged protests against the move to Stratford, including before the club's last home game against Manchester United.
Levy added: "As far as the fans are concerned, I have to say that it's a very, very small group of individuals who would make it clear that, whatever happens - even if we couldn't build a bigger stadium - they would want us to stay here.
"How do we get the next generation of fans to come to a game if they can't get a seat? It's a real dilemma for us."
Source: PA
Source: PA