Anthony Joshua says British rival Tyson Fury must lose two stones in weight before they fight.
The WBA-IBF-WBO world heavyweight champion is open to fighting Fury -- a former holder of the same three titles -- next year.
Joshua (21-0, 20 KOs), 28, defends his belts against Russia's Alexander Povetkin at Wembley Stadium on September 22 and a $15million deal has been made for American Deontay Wilder, the WBC titleholder, to then fight Joshua at the same venue on April 13.
But Wilder (40-0, 39 KOs) is not happy with the terms being offered for a unification fight and Joshua says he would be happy to fight Fury instead.
Fury (26-0, 19 KOs), 29, ended two-and-a-half years of inactivity last month, losing eight stones for his comeback after out-pointing Wladimir Klitschko in November 2015. Fury, who weighed in at 19st 10lbs for the bout with Sefer Seferi in Manchester, is due to fight again on August 18.
"Fury can be the size he wants to be," Joshua told reporters.
"There's no stopping him from stepping up. If the Wilder fight didn't happen, I would happily fight Fury.
"He's not in condition. He's still two stones over to when he fought Klitschko. Even though he's lost weight he's still two stones over his peak weight.
"When he's a couple of pounds over, half a stone over, then I'll say he's at his peak again.
"What does he do, two sessions a day? I would rather do two boxing sessions a day. Why would you do one boxing session and one run?
"Are you trying to be a part-time boxer and a part-time track runner? Get in the gym. Focus on your gym work. That's what Klitschko did. The best fighters spent more time in the gym than anywhere else."
Joshua does not believe Fury is serious when he says he is ready to fight him now.
"He was watching the Muhammad Ali documentary and thought it was Ali, Foreman and Fraser all over again," Joshua said.
"But it's not, it's a different type of boxing and he's not ready for that."
Another possible fight for Fury in 2019 if Wilder is not agreeable is against the winner of next Saturday's fight between England's Dillian Whyte and former WBO titleholder Joseph Parker at the O2 Arena.
Parker took Joshua to points for the first time as a professional on March 31 and Joshua has given Whyte, who he stopped in seven rounds in December 2015, some advice.
"All Whyte needs to do is focus on his cardio for this fight," Joshua told reporters.
"Different fights need different types of training methods I think.
"The Whyte that fought Lucas Browne in his last fight will struggle against Parker. Parker's very quick and nimble so you need to match speed for speed.
"That's how I managed to beat Parker, I beat him at range, I matched him speed for speed.
"If I was slow he may have walked away with the fight and that may be where Parker can cause Dillian a few issues.
"But if I want someone to win it would be Whyte because that would set up a future fight for us."
Joshua's preference is still for his rival champion Wilder to accept terms for boxing's first unification fight for all four major heavyweight titles.
"I don't honestly see a reason why the Wilder fight will not get made. It's like telling the kids there 'aint no Santa," Joshua said.
"I don't believe this fight shouldn't happen next if I get past Povetkin.
"We came close a few times to getting it done. We've actually got months and months of history to play with to get it done so I don't see why not.
"I've signed the contract already. When Wilder ranted with that social media stuff 'Hey man I'm signing the contract'. No, no, get it done, and then we'll announce it."