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A long touted fight between the pair has been on the cards several times over the years, but has failed to materialise for multiple reasons.
Fury was set to face Oleksandr Usyk in a proposed undisputed world title bout later this month, while Joshua defeated Jermaine Franklin earlier this month.
Hope for another round of negotiations with former two-time world champion Joshua had been mooted, but now Warren says no discussions have been had.
"I don't know the answer to that," he said. "The other side spoke a lot about wanting to reach out and contact us after the fight with Franklin.
"We've not heard anything, not had any contact, so there's been nothing to discuss with Tyson.
"They made it quite clear pre-Franklin fight that they wanted to maybe look at that fight for the summer. They thought maybe there was an opportunity.
"I haven't heard from them. I haven't had a phone call, I haven't spoken to anyone about it. You'd have to ask them."
Joshua, who lost twice to Usyk including in a rematch last year in Saudi Arabia, returned to winning ways against American Franklin earlier this month.
However, he has since indicated he will not fight again until December, leaving the rest of the heavyweight division to look for other opponents.
Fury meanwhile has not fought since a trilogy bout victory against Derek Chisora in December.