The highly-rated Zivkovic has established himself at Groningen this season, with the 17-year-old attacker scoring 5 goals in 20 Eredivisie appearances.
Ajax director of football Marc Overmars last week confirmed that the defending champions are interested in acquiring Zivkovic's services.
And Groningen chief executive Hans Nijland has now revealed that the two teams have entered discussions over a potential deal for the youngster.
"Negotiations are ongoing, so I cannot say too much about them," Nijland told Algemeen Dagblad.
"We wanted to extend his contract, but Richairo has shown to have ambitions. He wants to take a higher step. That's his right.
"But there is certainly no green light yet. After the weekend, we will continue talking. The talks with Ajax have been very enjoyable."
