However, the reigning WBA, WBO, IBF and IBO champ would still "love to fight Tyson Fury" at some point.
Following Fury's controversial draw with WBC king Deontay Wilder in Los Angeles last weekend, all the talk has been which heavyweight blockbuster would be next.
After that fight Fury, who described the result as "the biggest robbery in boxing, called AJ "a chicken" for dodging him and Wilder.
And while a rematch seems the most likely option, Joshua is seemingly still keen to sort a deal for an "all the belts" war against Wilder.
Speaking on the Alan Brazil Sports Breakfast on talkSPORT, Hearn said: “I’ve been hearing a lot of things that simply aren’t true.
“AJ’s first choice is Wilder because when you’re collecting belts, which he is, he wants to be the unified champ.
“He’d love to fight Fury as well, but for now I think Wilder is the one he wants.
“There’s three or four options at the minute for us.
“Sooner or later fight fans are going to get everything they want, but we won’t be doing any silly deals – that’s for sure.”
A TY-DY PROFIT
TYSON FURY’s dramatic clash with Deontay Wilder has pulled in the most paying viewers for a world heavyweight title bout in 15 years in the US, it has been revealed.
Saturday’s split-decision draw between WBC titlist Wilder and lineal champion Fury looks to have attracted over 300,000 pay-per-view buys in America.
That will make it the most successful world title clash between heavyweights in the country since Roy Jones Jr. beat John Ruiz to win the WBA belt in 2003.
The figure represents the number of homes that bought the fight on the Showtime cable channel in the US, and does not include UK television sales, or purchases through digital platforms.
SunSport reported how Joshua has once again laid claim to being the best heavyweight out there.
peaking to CNN World Sport, Joshua has now warned both men that he remains the King of the Heavyweight Jungle.
He said: “I’m not Wilder or Fury, none of them can box like me.
“None of them have what I have. His performance is his own performance.
“What I do want to do is make the announcement that April 13th is the day and Wembley is the venue, I’m more than willing to fight either one of them.
"I feel like after the fight, my name will pop up and because I don’t talk much people underestimate the passion I have to fight one of these guys. I’m willing.”
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