The IBF and WBA heavyweight champion is waiting to see if terms will be agreed with Klitschko for another bout after his thrilling stoppage victory at Wembley in April.
Hearn has held talks with Klitschko's manager Bernd Boente and told Sky Sports News: "We're getting close now to identifying the real options in terms of venues and locations.
"Vegas has taken a little bit of a front-runner 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 Boente this morning, I feel like it's going to take that special event to make this fight."
Hearn added his preference would be for Joshua to defend his titles on home soil but is excited by the prospect of taking the fight to Las Vegas.
"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..." said Hearn.
"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."
