Tottenham are comfortably in the driving seat to land the Ajax defender after he revealed a preference for a move to White Hart Lane earlier this month.
However Vertonghen, whose contract with the Eredivisie champions expires next summer, also expressed his concerns over the difference in valuation placed on him by the two clubs.
Spurs are reportedly unwilling to go above £10 million for a player who would be available for free next summer, while Ajax are said to be demanding a figure in excess of £12 million.
Now Levy has travelled to the Amsterdam ArenA to meet with officials from Ajax, and was pictured in De Telegraaf alongside Vertonghen’s agent, Mustapha Nakhli.
Ajax financial director Jeroen Slop and commercial director Henri van der Aat met with Levy to continue talks over the Belgian, and while the Spurs chairman is now back in England, it is believed that talks went well and a deal could be concluded sooner rather than later.
Vertonghen is believed to still be keen on a switch to White Hart Lane despite the fact Spurs will no longer be competing in the Champions League after Chelsea took their place in the tournament following their victory over Bayern Munich in the final on Staurday.