The 26-year-old has made a huge impression since being invited for a trial over pre-season and scored two goals on the club's tour of Scotland last week.
Gunn told the Eastern Daily Press: "We've made Goran and his representative an offer. I think he has got other offers on the table and he is currently thinking about those and ours.
"I think he is in Belgrade at the moment nursing his injury."
But Gunn has revealed fellow trialist Michael Bridges will not be offered an extended stay at Carrow Road, adding: "I've decided not to take Michael's situation any further.
"I've spoken to Michael's agent and I've received a nice text from Michael to say thank you for giving him the opportunity."