Levy is understood to have held face-to-face talks with Real Madrid president Florentino Perez, who has said he is willing to pay €100m (£86m) for Bale, in a deal that would eclipse the current world record transfer fee of £80million Real paid for Cristiano Ronaldo in 2009.
However the two clubs are thought to still be £14million apart, with Levy demanding a fee of £100million for his star man.
Levy has added he would be willing to listen to any offer that included young Spanish forward Alvaro Morato, although Real do not want to part with a player they believe will be a future star for club and country.
The prospect of any makeweight being included in the deal is unlikely, meaning the two clubs must find a way to bridge the £14million gap in the coming days.
Bale has had his head turned since hearing of Real’s interest, but has been encouraged by the fact Levy has been willing to hold talks with Perez.
The two men met in Florida while Real Madrid were in action on their pre-season tour, and are poised to hold further talks in the coming days.
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