The teenage FC Groningen star has been tracked by Liverpool and Manchester City over the course of the season, but reports coming out of the Netherlands claim Ajax are set to tie up a deal to bring him to the club in the summer.
Ajax director of football Marc Overmars reportedly held talks with Zivkovic's agent earlier this week and agreed a three-year deal for the player.
The Dutch under-19 international has been likened to former-Chelsea and Real Madrid winger Arjen Robben, and Liverpool and City were thought to be watching him closely.
He has made 20 appearances for Groningen so far this season, scoring five goals after he broke into the senior side last term.
The report claims Ajax will pay £2m to bring the Liverpool and City target to the Amsterdam club. Liverpool and City had reportedly been weighing up offers of their own but it looks like they will not get a chance.
The teenager can play up front or out wide, and is widely regarded to be one of the best young talents in the Eredivisie.