Joshua holds the IBF, IBO and WBA (super) heavyweight belts after knocking out Klitschko in the 11th round of a thrilling contest at Wembley Stadium in April.
Last month, Hearn confirmed Las Vegas was the front-runner to host a rematch and it now appears an official announcement of the fight's location and date may not be long in coming.
Hearn told Sky Sports News: "I've been in Vegas with AJ, officially applying for my Nevada boxing license to promote there and that went well.
"I met with the MGM and met with the T-Mobile Arena. Vegas is the front runner and November 11 is the date that is pencilled in.
Quiet Night Out ~ USA pic.twitter.com/rfpPmsEbA7
— Anthony Joshua (@anthonyfjoshua) July 23, 2017
"It will probably take a couple of weeks to get everything over the line, but I believe Klitschko will take this fight and believe Vegas will be the one.
"The amount of British fight fans that would travel there, it will be a momentous occasion and one that we will savour for a long time so fingers crossed it's a party in Las Vegas on November 11."
Stephen Espinoza, head of American broadcaster Showtime, added: "It's no secret we've been salivating about getting him over here and certainly that would be a phenomenal fight.
"It would be the biggest heavyweight Vegas fight in probably a couple of decades, so we would love to host it."
Photo: Getty Images (Anthony Joshua lands a fearsome uppercut on Wladimir Klitschko during their April bout)