Joshua retained his IBF crown and gained the WBA and lesser-regarded IBO belts by stopping Klitschko in the 11th round of an epic battle at Wembley Stadium in April.
The champion is awaiting a decision on the second bout from the 41-year-old Ukrainian, who hinted at retirement following just his fifth career defeat in London.
Promoter Eddie Hearn has held discussions with Klitschko's manager Bernd Bonte and feels a Las Vegas bout could be the key to locking the fight in, though Nigeria, Dubai and Cardiff are also in the hosting mix.
"I have been in talks with Bernd Bonte and the team. We're getting close now to identifying the real options in terms of venues and locations," Hearn told Sky Sports.
— Joe Cordina (@JoeCordina_91) June 27, 2017
"Vegas has taken a little bit of a frontrunner in those. I know the British fans would love to do a trip out there for Joshua-Klitschko.
"Nigeria is still in the mix, Dubai as well, and of course Cardiff. But like I said, Vegas has probably got its nose in front at the moment.
"I think in the next week, we're looking to present all those opportunities to Wladimir Klitschko and his team. Speaking to Bernd Bonte this morning [Wednesday], I feel like it's going to take that special event to make this fight.
"I would like to keep it in Britain. The fans have been incredible to Anthony Joshua, but if it means travelling to make sure this fight happens for world boxing, and it means taking a few plane loads to Las Vegas for a night and an experience they won't forget.
"Anthony Joshua is the world heavyweight champion, he's not the British heavyweight champion. He wants to break boundaries and so do we.
"To see Anthony Joshua's name up in lights on the Las Vegas strip is certainly something that appeals to us all.
"I would say the next couple of weeks, we'll be looking to make a decision in terms of the venue and location."