Spurs have been heavily linked with the French goalkeeper throughout the summer, with a fee of £12 millions being agreed between the two parties.
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However, the Ligue 1 club's chief has hit out at how Levy has handled the transfer, claiming the Premier League outfit have changed stance over certain agreed aspects of the move.
Aulas told reporters: "We have had people speaking all night with Daniel Levy. He talks a lot and goes back on what we've agreed in writing.
"The things as they were at 5am were not the same at 10am. I think we have to make sure we get a certain amount of value because it's important that Hugo can go to a quality club that allows him to do himself justice from a value point of view, so that he can feel right about it.
"At the moment we're talking about whether he can come back to say his goodbyes to the supporters, to his team-mates, so we can honour him, this truly great player and brilliant man.
"I would put it at 50-50 that Hugo goes to Tottenham. Although from the outset we've submitted to agreements I would now put it at 50-50 that he'll be going there.
"Agreements have not at all been respected. We've done what we can. Hugo has been troubled by the difficulty in these negotiations.
"He's one of the best in Europe in his position. Our transfer window is open until 4 September but for Tottenham the English transfer window closes on 31 August.
"Either it happens tonight or not at all for Hugo Lloris."
Aulas, who is himself known for being a notoriously tough negotiator, revealed that the keeper has agreed personal terms but is still not convinced on a switch to north London, adding that the ongoing talks have been the hardest in his 25-year career.
"It's been very, very difficult," he continued "I've got 25 years of experience as a president of a club and it's our 16th participation in a European competition in a row. But this is very rare in the football world.
"The negotiation with the Tottenham directors has been the hardest I have ever had to undergo in these 25 years.
"We had email exchanges which have been contradicted, so that's made it very complicated. It's difficult. The Tottenham board's theory is to explain that the economic market is very hard and so we have to get used to renegotiating.
"But for us, who are attached to a player of the quality of Hugo Lloris, and such is the value of the transfer, that causes us to ask questions.
"He has agreed personal terms with Tottenham, he remains under that impression, but since we have had Hugo Lloris on the telephone for a long time overnight and this morning and he's completely undecided about what happens next.
"We've been negotiating all night. The first negotiation was at the start of the window, about a month-and-a-half ago, through an intermediary who was a French lawyer, who lives in Lyon.
"And then nothing for about a month-and-a-half. The negotiation then picked up again about a week ago."