Tyson Fury recently declared he was "unstoppable", but heavyweight rival Dillian Whyte claims to have floored the WBC champion on "multiple occasions".
Whyte is scheduled to receive a mandatory shot at Fury's world title by February 2021 at the latest.
But he must first wait until the champion has taken on American Deontay Wilder for a third time.
There is also a strong push for Fury to face Anthony Joshua in a unification contest after that, but Whyte is tired of being the odd man out.
Whyte, whose only career defeat came against Joshua in 2015, feels Fury would have fought him already if he did not know he would be in for a testing outing.
"He just needs to stop talking rubbish and let's have a go," Whyte, who is preparing to fight Alexander Povetkin next, said about Fury to Sky Sports.
"It will be a major fight. Let's have it out.
"He's the one who came out and said he beat me up in the gym and stuff like that. I can tell you now, that didn't happen. I don't like telling sparring stories, but people in the game know.
"They know about me. Me and Tyson Fury sparred and I bashed him about and dropped him on multiple occasions. Simple as that.
"If I was such an easy fight, why is he not in any rush to fight me?
"He said before beating Wilder, when I beat Wilder, I'm going to give Dillian Whyte his title shot. He just talks rubbish, I'm just sick and tired of it. This is war, let's go."
Undefeated Fury has recently ended talk about retiring in the near future and is now targeting a long title reign.
Whyte's promoter Eddie Hearn believes Fury should take on the challenge and urged the WBC to ensure it happens.
"We've got to push that with the WBC," Hearn said. "I would love to see Fury step up and fight Whyte, but I understand he has contractual obligations with Wilder.
"Dillian is right in the mix and we will fight his corner. We've been promised by the WBC and we expect them to stand by it. We've done all we can in that respect.
"He stayed patient and has been given a time of February 2021. It is public, so they will look very silly if it doesn't happen.
"If, for some reason, Wilder is not available to fight Fury, then Whyte must get that fight now.
"Why not? It's an unbelievable fight, two Brits fighting for the WBC title."
IBF, WBA and WBO champion Joshua would be waiting in the wings, and Hearn added: "Then [there would be] a cast-iron certainty of two Brits fighting for the undisputed championship in 2021."