Joshua and Fury have been considering several offers from countries bidding to stage the blockbuster all-English showdown, with Saudi Arabia the long-term frontrunner.
Fury confirmed last week that there were “three or four big offers” on the table to host the first fight in July, with interest from Qatar, Uzbekistan, Russia and America as well as the UK, with London Mayor Sadiq Khan insisting last week that London could host the bout.
Hearn, who met Fury on Tuesday, says the two fighters have “approved” a site offer but is yet to confirm a date and venue.
Hearn told Behind The Gloves: “Both sides have approved the site offer that they want to go with, and now we are just finalising the site deal and we are in a great place.
"I saw Tyson yesterday. I just messaged him and said, 'I'm in Vegas, I'm in your hotel if you fancy a cuppa'.
"We just had five or 10 minutes together and it was good, because I don't represent Tyson Fury, so I don't know what is in his mind. What he basically cemented in my mind was, this is the only fight he wants, and I know that's the same with AJ.
"It just good to say, right we've got the offer, we all approve. We're moving forward now. We're good.
"It has been agreed by both sides, the option that we will take, and you'll get the date very soon and the official announcement."