Speculation of a big-money showdown between the pair has stepped up following the Gypsy King’s stunning knockout victory over Deontay Wilder in Las Vegas last month.
That win has paved the way for a huge unification fight between the pair with Joshua currently in possession of the WBA, WBO and IBF belts after he defeated Andy Ruiz Jr in their rematch Saudi Arabia in December.
Joshua is scheduled to fight Kubrat Pulev in June while Fury is expected to fight Wilder again but, if they keep hold of their titles, Tyson is backing them to come to blows at last.
Tyson, who was the first heavyweight to hold the WBA, WBC and IBF belts and later became the lineal champion, said in an interview with The Sportsman: ‘They’re in the best shape possible to be in and getting the most out of this sport as they can.
‘I don’t know, but I’d like to see that happen, though.
‘That’d be a great money fight too!’
But any chance of Fury being allowed to compete again is in danger following news that UK Anti-Doping will investigate him and his cousin Hughie Fury after allegations that a member of their team offered a farmer £25,000 to lie about how they each failed a drugs test in 2015.
If the Furys are found guilty of a potential new charge of tampering with the initial investigation – which led to backdated two-year bans for the Furys in 2017 for their nandrolone positives – then they would each be facing possible eight-year suspensions for a second offence.
But Joshua‘s next world heavyweight title defence against Pulev is also up in the air after it emerged it could be pushed back a month to July due to the coronavirus outbreak.
Hearn, whose Matchroom organisation earlier confirmed the postponement of all boxing events in March and April, once again dismissed the prospect of any of his major bouts being staged behind closed doors.
Referring to the June 20 date, Hearn told Sky Sports News: ‘At the moment it’s still in place.
‘Obviously with the news of the Euros being cancelled (Euro 2020 has been postponed until next year) and the possible extension of the Premier League season, Spurs may need that stadium in June.
‘We do have an option to run that fight in July as well at the same stadium. Everything now is really a case-by-case situation and a day-by-day situation of trying to think on your feet.
‘June 20 is a long time away, it’s still in our plans and we have been speaking to Tottenham to make sure we’re all on the same page and that we know we have the same strategy moving forward.’