According to Ivaylo Gotsev, manager of Kubrat Pulev, the bout with Anthony Joshua will need to finalize a new location within three weeks.
Joshua was scheduled to defend his IBF, IBO, WBA, WBO world titles against Pulev on June 20th at Tottenham Hotspur Stadium in London.
The date was pushed back due to the ongoing coronavirus pandemic.
Eddie Hearn, who promotes Joshua, had been targeting a date in late July. That likely won't happen at this point.
Gotsev recently mentioned the possibility of taking the fight to a location in Croatia.
Time is running out, says Gotsev, with only a few weeks remaining to select a new location.
"We've given ourselves four weeks to explore any and all opportunities that are there for the fight," Gotsev told Sky Sports.
"Eddie has spoken to you about the Middle East, which is a great possibility. It makes sense, because those countries were not as hard affected and if you take the right precautions, we could really have a safe environment. That's something I want to emphasise, and I can't say it enough times - safety first. We don't want to take a risk against anyone's health, no way no how.
"Whatever makes most sense, wherever we can have the best conditions under the current terms we're living in, that's where we're going to go in. There you have it, we have about three more weeks left on the exploring and then we'll see where the best options lie."
If the UK is capable of hosting the fight, Gotsev says there is no problem with taking the fight back to Joshua's backyard.
"We were willing and we actually agreed to come to the UK, so that's never been a question of neutral ground," said Gotsev.
"It was Joshua's demand, 'I want to go back home.' Okay Joshua, you're the champ, we respect that, we're coming to the UK. Kubrat is coming there to kick your ass, in front of your crowd. No problem. They are fighters, it's one against the other. At the end of the day, the public can jump, scream and shout, but it's man e mano in the ring, we've worked out that. To us, it didn't matter that the fight is taking place in the UK."