The 48-year-old is currently in charge of FK Rad after spells at Serbian sides Sindelic Beograd, Zemun and Cukaricki in recent years.
Since stepping into the dugout, he has enjoyed a string of successes in saving clubs from the drop whilst working with limited budgets.
And Herald Sport understands that Petric is on the list of candidates to replace Lee McCulloch at Rugby Park as he looks to clinch a return to Scottish football.
The likes of Jim McIntyre and Gary Holt have been linked with the position in recent days but Petric has now emerged as a contender for the post.
Academy Director Paul McDonald has been placed in charge of first team affairs and will take his side to Firhill this weekend to face Partick Thistle.
And it is understood that the Killie board are in no rush to do a deal as they continue to consider their options over the key appointment.
Petric, who was part of Rangers’ nine-in-a-row winning side and also had spells at Dundee United and Hearts, moved into management five years ago after stints as general secretary and vice president at Partizan Belgrade.
And in an exclusive interview with Herald Sport in May, the former Yugoslavia internationalist admitted he would consider a return to Scotland to continue his coaching career.
“If somebody gave me a choice between working in Spain and working in Scotland I would choose Scotland,” he said. “It was a great time for me.
“I saw a totally different side to the game from when I had played with Rangers, Dundee United and Hearts when I was the general secretary at Partisan.”
Petric has spent time with the likes of Jose Mourinho and Carlo Ancelotti in recent years in a bid to expand his knowledge of the game.
And now he could put his experiences to good use at Rugby Park if he is given the chance to save Killie from the Premiership drop.