The fight is scheduled for April 1 at the O2 Arena, London.
“I don’t do the online discussions just for clout, so if you’re really about it, shout @258mgt,” Joshua replied to Fury. “I’ll be ready in December.”
If the fight did happen, the winner would become the first undisputed heavyweight champion since Lennox Lewis from 1999 to 2000.
Joshua was defeated by Ukraine’s Oleksandr Usyk on a surprise split points decision after 12 hard rounds to retain his WBA, WBO, IBF and IBO world heavyweight boxing belts in Jeddah.
“I am convinced he wants to fight me. I want to fight him. And if I’m not fighting Tyson Fury, I’m not fighting at all,” he said.
“Champs f$ck up sometimes… but we bounce back and come with vengeance!!,” Usman tweeted.
The Ukrainian champion defeated Joshua after 12 rounds in a split decision of 113-115, 115-113 and 116-112 at the arena in Jeddah, Saudi Arabia.
In a video of himself doing press-ups posted on Twitter, Joshua wrote, “Out my hands and leave in God’s,” adding a meme of hands lifted in prayers.
“If you know my story, you know I’m the comeback king. You can put me down, but it’s difficult to keep me down,” said Joshua.
Usyk beat Joshua in front of a sell-out crowd in London in September last year to claim the WBA, WBO, IBF and IBO belts.
