Joshua's world heavyweight title reign and unbeaten record were ended by a stunning defeat to Ruiz Jr. in New York earlier this month and Hearn has activated a clause to enforce an immediate second fight, Sky Sports News reported.
The British star's team are considering a number of British venues, including Wembley Stadium for a date in November or December, but the Matchroom Boxing boss has confirmed that Joshua is still open to the idea of staging the return bout at the scene of his first defeat.
"The job over the next week is just to finalize the details now of just where and when that will be," Hearn told Sky Sports News.
"I can't tell you too much, just because I don't know other than, between November 16 and December 14 will be the date of the fight. We've had offers from five different countries to stage the fight. For me, it's a straight decision between the UK or America.
"In the UK, we're talking to Cardiff, to Wembley, to Tottenham and in America, we've had a couple of approaches, but our preference is Madison Square Garden.
"A sensible man would say 'Do it in the UK'.
"Anthony feels as though it would be special to rewrite history and get the win at Madison Square Garden. It's really not about the money so much, it's just about where we believe this fight should take place and those decisions will be made in the next week."