The highly-rated midfielder has been a target for Andre Villas-Boas throughout the transfer window, and he has increased his interest with Gareth Bale now looking certain to join Real Madrid.
Spurs chairman Daniel Levy was in Amsterdam on Wednesday to discuss a possible deal for Denmark international Eriksen, who has just one year left on his current contract, and it appears that the talks have progressed well.
"Yes, Levy was here and Eriksen has been given permission to speak to Tottenham," Ajax director of football Marc Overmars told De Telegraaf.
Spurs are believed to have tabled an offer in the region of £8m for the 21-year-old, although Ajax are thought to be demanding a fee of £12m.
"There is no agreement yet until it's signed," Overmars added.
"Obviously, if it happens, we won't be happy at all to lose him but he only has a year left on his contract."
Ajax signed Eriksen from Danish club Odense Boldklub in 2008 and he has since gone on to establish himself as one of the most promising young midfielders in Europe.
Tottenham defender Jan Vertonghen, who used to play with the Dane at Ajax, thinks Spurs will be signing a top talent if the deal goes through.
"He is a good guy," said Vertonghen, who moved from Ajax to Tottenham last summer. "I played with him for four years and he is a good player."