Spurs have been chasing Eriksen for a while and they have stepped up their interest in the Dane following the news Gareth Bale is close to sealing a world-record move to Real Madrid.
Tottenham chairman Daniel Levy was in Amsterdam on Wednesday to discuss the possibility of signing the midfielder, 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.
Tottenham are reported to have offered around £8million for the 21-year-old, but that falls someway short of Ajax's £12million valuation.
"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."