On Saturday, Joshua added the WBA belt to his IBF title with a dramatic 11th-round stoppage of Klitschko in front of an estimated 90,000 crowd at Wembley Stadium.
"Fury where you at, baby?" Joshua said while still in the ring. "I love fighting. Tyson Fury, I know he's been talking, I want to give 90,000 a chance [to see us], I just want to fight."
Fury, who has been inactive since his 2015 win over Klitschko having most recently struggled with depression, responded to Joshua's comments by taking to social media.
@anthonyfjoshua challenge accepted. We will give the world 🌎 the biggest fight in a 500 years. I will play with u. You are a boxers dream.— TYSON2FASTFURY (@Tyson_Fury) 29 April 2017
Both Fury and Joshua are unbeaten in their professional careers.