Spurs chairman Levy was pictured at the Amsterdam ArenA earlier this week and Vertonghen has confirmed he has spoken with all the club's 'key' people.
However, after Spurs missed out on qualification for next season's UEFA Champions League, the Belgium international is concerned the club will be unable to agree a fee, with Ajax demanding €15million (£12.5m).
The 25-year-old has just one more year to run on his current contract with Ajax and will not cause any ructions with the Dutch champions if a deal cannot be reached.
Vertonghen, though, also concedes that joining Spurs' arch-rivals Arsenal is a possibility after talks over a move to White Hart Lane failed to progress.
Lot of money
"I've said repeatedly that Tottenham are my first choice, but the talks haven't progressed," the centre-back is quoted in the Daily Star.
"They have shown me around, I have met all their key people and their chairman came to meet me on Monday.
"But Arsenal want me too. They remain a possibility if my Spurs move falls through, as Ajax are asking €15m for me. That is a lot of money for someone with just a year left on his contract.
"I'm sure Spurs won't be able to pay that much after they missed out on the Champions League.
"Ajax want to get as much as they can for me, while Spurs want to pay as little as possible.
"I hope a deal can be done. But I won't fight with Ajax, that is the last thing I'd want after so many good years with them.
"England is my preferred destination. But if needed I will see out my contract and leave on a free transfer next year."
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