Pérez, the Madrid president, said at the meeting that his club are prepared to pay €100m (£86m) for the Wales forward, which would eclipse the current record – Cristiano Ronaldo's £80m move from Manchester United to Real in 2009. But Levy, the Spurs chairman, wants £100m.
Levy added that he would be prepared to do business if Pérez included the highly rated young Real striker Alvaro Morata in the deal. But Real do not want to lose a player whom they consider to be a future Spain No9.
The prospect of any makeweight helping to finalise the transfer is complicated and, as such, unlikely. The challenge in the coming days will be for the two parties to bridge the £14m gap in their respective valuations, to facilitate a straight cash deal.
Pérez and Real were in Florida for the club's pre-season friendly against Chelsea while Levy has a property in the US state. Talks will continue but Bale, who is desperate to be granted his dream move to the nine-times European champions, has been encouraged by Levy's willingness to entertain Pérez.
Bale's focus has been affected by the situation and he has not played for Tottenham since their opening pre-season friendly against Swindon Town on 16 July. He travelled to Hong Kong for the Barclays Asia Trophy, at around the time that Real escalated their push to sign him, and he did not play in the matches against Sunderland or South China.
He did not travel to France for last Saturday's game against Monaco and he will not feature against Espanyol at White Hart Lane on Saturday. The official reason for his absence is a gluteal muscle injury and, subsequently, a minor foot problem.
Chris Coleman, the Wales manager, has called up Bale for next Wednesday's friendly against the Republic of Ireland in Cardiff but his involvement is in considerable doubt.
"I am sure with what is going on in terms of the transfer, there is a lot on Gareth's mind and Tottenham's mind," Coleman said. "Whatever is going to happen is up to Tottenham and Gareth. We have picked the squad and he is in it. Unless we are told that he is unavailable we will just do what we've always done, and that is expect him to be there. You have to look at it and say: 'OK, there is a lot going on.'
"He is a quality player, whether he is in the Premier League or anywhere else. He is only 24 and he is only going to get better. I don't think it is Gareth's fault or a player's fault that a club is willing to pay that type of money as a transfer fee. It is out of the player's hands.
"The money we are talking about is incredible but that is not Gareth's fault. If clubs are willing to pay huge transfer fees and huge salaries, it is up to the clubs."
The Toulouse president, Olivier Sadran, has claimed that Tottenham are on the brink of signing the midfielder Etienne Capoue from the French club. André Villas-Boas, the Tottenham manager, is prepared to listen to offers for Tom Huddlestone and Scott Parker, and Sadran suggested that the north London club were ready to beat Cardiff City and Atlético Madrid to the signature of Capoue. "He will go there," Sadran told Radio Monte Carlo. Capoue, who had previously attracted the interest of Arsenal, is rated at €11m.
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