The 17-year-old has impressed this season, scoring five goals in 20 top-flight appearances for the mid-table side.
The striker's contract at Groningen runs until 2016 and they are keen to keep hold of him.
But Zivkovic has reportedly been attracting interest from across Europe and Ajax are unlikely to be the only club lining up a bid.
"Zivkovic is an interesting player that we are indeed following," Overmars told Voetbal International.
"Dutch players are our preference if we look for possible reinforcements.
"During the Eredivisie you see a handful of players emerge and Zivkovic is one of them."
Zivkovic has made three international appearances for the Netherlands Under-19s, scoring twice against Moldova and Georgia.
