Vertonghen's representatives met Ajax officials with the aim of resolving the dispute, which is holding up his transfer to Tottenham.
It is understood the Belgian, who is in the final year of his contract, believes he is entitled to a cut of the reported £9million transfer fee, but Ajax disagree.
The 25-year-old is desperate to join the north London club despite reporting for training with Ajax this week, but the meeting with the Dutch team was not successful.
Vertonghen's agent Mustapha Nakhli told Press Association Sport: "We have nothing (agreed) at this moment.
"They (the talks) were not easy but we are going to try again, maybe tomorrow [Saturday]."
Nakhli had sounded confident a deal could be struck on Friday when his agency released a statement to De Telegraaf which read: "We have a meeting with Ajax at the end of this morning to come to a solution.
"There is some movement and we have the intention to come to an agreement."
Although the deal is by no means dead in the water, the fact the talks will drag on into a second day is frustrating for new Tottenham boss Andre Villas-Boas, who wants to make the centre-back his second signing at the club.
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The Portuguese has already snapped up Gylfi Sigurdsson from Hoffenheim and he is determined to add more youthful players to the ranks.
Brazil midfielder Oscar, 20, confirmed Tottenham have contacted him about a potential transfer from his current club Internacional.
"They (Tottenham) contacted my agent," Oscar told Brazilian website Lancenet.
"I do not know if there was an official proposal, you'll have to ask my manager or the president.
"I don't know what might happen, I'm not thinking of it right now.
"Not only Tottenham [asked about me], but I'm not sure if there was an official offer. Offers always come for me, [team-mate Leandro] Damiao and whoever is showing up."