Anthony Joshua lost his IBF, WBA and WBO titles in a stunning upset loss against Andy Ruiz Jr at Madison Square Garden in New York last month.
The Briton – now 22-1 – exercised the clause in their fight contract for an immediate rematch later this year.
But the official announcement of the second bout has been delayed amid uncertainty as to where exactly Joshua and Ruiz will trade blows.
A return to MSG has been touted for November while Cardiff’s Principality Stadium – which holds near 80,000 fans when it hosts boxing – is another potential venue in mid-December.
Joshua’s loss to the Mexican was his first ever professional fight outside of the United Kingdom, having fought in front of capacity crowds at the Principality Stadium and Wembley Stadium in his previous four scraps.
And despite Joshua previously indicating he wanted to avenge his defeat at the very same scene in the Big Apple, Hearn insists the fighter has no preference.
“Anthony doesn’t care where he has it, but he has to make the decision and I am not making it for him,” the Matchroom Sport chief said.
“Common sense will tell you home is better than away, in any sport.
“There is also an option to have it at Madison Square Garden in New York.
“But we will be alerting Andy Ruiz’s team this week as to where and when the fight will be and Cardiff is currently the front runner.”
Speaking to Sky Sports last week, Hearn implored Joshua to pick a location that will allow him to get in the right frame of mind.
He said: “For me, it’s got to be where ‘AJ’ is comfortable. There’s no point ‘AJ’ saying to me, which he’s continually says, ‘Ed, do it where you want. I’m easy’.
“No, no, no. This is too big for me to make a call on. You have to decide.
“There’s a lot more money to do it in America. I promise you, the money ain’t even coming into it for him right now. I said, ‘You got to do it where you feel most comfortable.’”
Joshua had been gunning for a fight with unbeaten WBC champion Deontay Wilder before his loss to Ruiz but is confident he can right the wrongs of his loss and get his bid to become undisputed heavyweight champion of the world back on track.
“I think I can get it right, and that’s I’m taking the rematch and activating it immediately,” said Joshua in a 16-minute video on his official YouTube channel.
“True failure is in quitting, I don’t think you should give up when you meet a blip in life.
“Ruiz, I feel like I can get it right. That’s why I wanna take this rematch.
“My ambition in boxing at the minute is to be two-time heavyweight champion of the world.
“It is a small blip. This is my career. I am still keen to fight the best in the world and prove myself.”