Joshua is scheduled to defend his world heavyweight titles at Wembley Stadium on April 13, with Deontay Wilder, Tyson Fury, Dillian Whyte and Jarrell 'Big Baby' Miller all being linked with the British star, Sky Sports reported.
Wilder and his team have been ordered by the WBC to open rematch talks with Fury following their controversial draw in December. Hearn insisted there is "radio silence" from the 'Bronze Bomber', but he has spoken to Fury.
Whyte turned down the initial offer to become Joshua's IBF, WBA and WBO challenger in April and with Brooklyn's Miller behind those three, the promoter is expecting to make an announcement in the next seven days.
"There is radio silence from Wilder, Fury we're talking to and Whyte we're talking to," he told DAZN.
"He (Whyte) has got his price tag, Anthony's got the price tag he wants to pay. It's a voluntary shot for Dillian Whyte, and part of me would love to see Anthony Joshua come to the States.
"'Big Baby' Miller is creeping into the top five right now. He's making some noise in America and to be a global star at some time, you have to fight in America.
"And to see Anthony Joshua fill up Madison Square Garden, with 21-22,000, that is a real statement of intent for a heavyweight world champion, for a Brit especially, so we'll see what happens.
"I think you'll get a decision next week. For me, if he can't get Wilder, Fury or Dillian, he must come to America and Jarrell would be at the front of that queue."