The British boxers are set to clash later this year but a date and venue for the bout are still to be confirmed, although the promoter is adamant that it will take place as long as both men win their warm-up bouts.
Warren told Sky Sports: "It's on, the fight is on - unless either of them get beaten in these two fights, they're going to have the fight is on, no problems.
"The one thing is they've both signed up for a fight. AJ's got his fight in July, and Tyson I believe will have a [warm-up] fight, I don't know where it will be yet or the date for it and once they're out the way their fight will go late autumn.
"I don't see any problems in getting this fight on. Everybody will be satisfied. Let them get their respective fights out the way - once that's done, then there will be an announcement."
Joshua will take on Kristian Prenga next month and his promoter Eddie Hearn says a defeat for the former heavyweight world champion could scupper hopes of a fight with Fury.
The Matchroom chief told Sky Sports: "In my opinion if either fighter loses, you cannot do the fight.
"I will feel sick at the ringwalk on July 25. Especially with what AJ's come back from. I mean there is that worry. Will he be the same? Everything we see in camp and in sparring lends us to suggest yes. But there's a lot to overcome. That's the importance of this fight as well in July."
Hearn added: "Now we have signed to fight Tyson Fury. He has signed to fight Anthony Joshua. The only thing that stands in the way is July 25."