The promoter also expects the IBF and WBA heavyweight world champion to box around the world, providing he gets through Joseph Parker, on March 31, live on Sky Sports Box Office.
Hearn, who is in Carson, California, for Scott Quigg's world title fight against Oscar Valdez, admits Joshua does not have to fight across the pond but will if he wants to become a global star.
"As a heavyweight world champion and a major star in world boxing, [Joshua] should box over here at some stage," Hearn told Sky Sports.
"There's always been that myth really that in boxing you have to crack America, but I don't see why.
"Look at what we are doing in the UK, look at the spectacles we are creating, [Joshua] is very happy boxing in the UK.
"I just think it's a natural progression to fight in other countries and he wants to break down boundaries as well and part of that should be boxing in America, Africa, the Middle and Far East, but right now he is very comfortable doing what he's doing.
"I am not sure if the US is imminent but I would expect him to box in America in the next 12 months."
WBC world champion, Deontay Wilder, who will be heading to Cardiff to be part of the Sky Sports Box Office team, and New York heavyweight Jarrell Miller, are just two big-name Americans who have already been mentioned as opponents for Joshua.
Skysports