The world number one struggled with his serve before falling to Italian Lorenzo Musetti in Monaco.
"The elbow is not in ideal condition, but let's say it's good enough. Hopefully, it will be fully ready for the first match," said Djokovic, who had elbow surgery in 2018, ahead of this week's event in Banja Luka.
The Serb won the Australian Open earlier this year to draw level with Rafael Nadal's men's record tally of 22 Grand Slam titles. He will be among the favourites for next month's French Open.
Djokovic will face 87th-ranked French teenager Luca van Assche, who ousted Swiss veteran Stan Wawrinka 1-6, 7-6 (7/4), 6-4 on Monday, in the Banja Luka second round.
"I've never met this boy before, I don't know much about him. I know he's young, he's just joined the top 100," said Djokovic before the tournament which has been relocated from his hometown of Belgrade because of work on the venue.
"I sincerely thought that Wawrinka was going to win today, he was leading most of the match. So it's indeed a surprise, the victory of this little guy, this Frenchman."
Van Assche battled back against former world number three Wawrinka, 20 years his senior, who has dropped to 84th in the world.
"It will be incredible for me and I'm only 18," he said of playing Djokovic.
"I know that the crowd will not be with me, I think, but I will enjoy it and I will try to win."
