Fury has consistently made jibes at Joshua's expense, claiming in January that he would knock out his fellow Brit within two rounds. Last week he said he had stopped training after becoming tired of waiting for the fight to be agreed.
Plans for a "Battle of Britain" have accelerated after Joshua, 31, stopped Bulgarian veteran Kubrat Pulev in the ninth round at Wembley Arena on Saturday to retain all three of his belts.
Joshua has a 24-1 career record as he continued to prove his shock defeat to Andy Ruiz Jr in June last year was an aberration.
Former Olympic champion Joshua defends his IBF, WBA and WBO belts at Wembley Arena against the veteran Bulgarian in front of 1,000 fans, limited in number by coronavirus restrictions.
Joshua pointed a finger in Pulev's face as they exchanged words while beefy security guards kept the peace during their weigh-in for Saturday's bout.
An agreement is in principle for Fury to fight Joshua twice in 2021 should Joshua come through his world title fight with Kubrat Pulev at Wembley on Saturday.
Mike Tyson, the 54-year-old former world heavyweight champion, is due to fight for the first time in 15 years when he meets Roy Jones Jr, the 51-year-old four-division world champion
Whyte was next scheduled to be in action on 21 November but a rematch with Alexander Povetkin was scuppered when the Russian tested positive for coronavirus.
Britain's Joshua was originally scheduled to fight Pulev on 20 June, with a second date in July also mooted amid the coronavirus pandemic.
Heavyweight champions Anthony Joshua, Tyson Fury agree financial terms for two-fight deal, says promoter Eddie Hearn
Joshua holds the WBA, IBF, WBO and IBO belts, while Fury is the reigning WBC champion.
Premier League: Watford captain Troy Deeney won't resume training out of concern for family's well being
Troy Deeney said, 'My son is five months and he’s had breathing difficulties. I don’t want to come home to put him in more danger.'
Coronavirus Outbreak: Boxing promoter Eddie Hearn planning to organise fights in his own back garden
Heavyweight world champion Anthony Joshua’s promoter Eddie Hearn is planning to organise fights in his own back garden when professional boxing returns in July from the COVID-19 lockdown.
Anthony Joshua will fight only once this year but might take on Tyson Fury twice in 2021, says promoter Eddie Hearn
Joshua, the WBA, WBO and IBF champion, is due to fight Bulgarian next while Fury, the WBC champion, has a rematch due with American Deontay Wilder.
Coronavirus pandemic: Anthony Joshua's heavyweight title defence against Kubrat Pulev could be moved to July, hints promoter Eddie Hearn
Anthony Joshua’s world heavyweight title defence against Bulgarian Kubrat Pulev at Tottenham Hotspur’s stadium on 20 June could be postponed to July due to the coronavirus outbreak, promoter Eddie Hearn said on Tuesday.
Tyson Fury's promoter looks forward to all-British bout with Anthony Joshua, but will wait for Deontay Wilder's call on rematch first
Tyson Fury’s promoter Frank Warren wants the new WBC heavyweight champion to fight fellow Briton Anthony Joshua next in a world title unification bout but says Deontay Wilder will first have to be persuaded to forgo an immediate rematch.
'London's calling', says Anthony Joshua who is likely to defend heavyweight titles at Tottenham's new stadium
Anthony Joshua is set for a London homecoming to start his second reign as world heavyweight champion, with his next fight likely to take place at the recently built stadium of Premier League club Tottenham.
Eddie Hearns defends decision to stage Anthony Joshua vs Andy Ruiz Jr rematch in Saudi Arabia, says match could 'change boxing forever'
Hearn insists it is unfair to criticise boxing for heading to Saudi Arabia, where Britain's Amir Khan also recently fought, because there are so many other sports organisations using the country now
Anthony Joshua to face Andy Ruiz Jr before end of year in rematch, according to promoter Eddie Hearn
Anthony Joshua will attempt to reclaim his heavyweight titles from Andy Ruiz Jr before the end of year after activating a rematch clause in his contract, promoter Eddie Hearn said Tuesday.
Underdog Andy Ruiz Jr. beats Anthony Joshua in shock victory at Madison Square Garden to become three-belt heavyweight champion
Joshua (22-1, 21 KOs) had a massive height and reach advantage as he weighed in at a chiselled 247 pounds (112.4 kilos) alongside the portly Ruiz, who beefed up to 268 pounds compared to 250 for his most recent fight
Eddie Hearn says in a Twitter post that Joshua's camp has been informed by the Voluntary Anti-Doping Association that there was an adverse finding in a sample collected from American boxer Jarrell Miller on 20 March