Joshua’s promoter Eddie Hearn announced on Monday that both heavyweights had signed contracts to meet again on December 7.
But Ruiz, who shocked the world when he stopped the Brit in New York in June, wants the second instalment to take place in the United States.
He said: “I know everybody is talking about the fight and all that but we got real news coming soon.
“Of course [I’m taking the rematch] but it’s going to be on our terms; we’re going to bring it back to the United States.”
While answering fans’ questions on Instagram , he accused Joshua of being “scared” and added: “Why do you think he’s over there trying to make the fight in Saudi Arabia?
“Like I said, I don’t have any protection over there, so if the United States of America wants to… never mind, I can’t say nothing.
“The fight is going to happen soon.”
Joshua wanted to host the rematch at the Principality Stadium in Cardiff but Ruiz refused to travel to the UK – despite being contractually obliged to.
Hearn also fielded offers from Dubai, Qatar and the United Arab Emirates before settling on Diriyah, near Riyadh.
The promoter said: “Both fighters have signed for this rematch and all governing bodies have been informed.
“There was a lot of talk about where this fight would be held but we wanted to go somewhere who believed in the sport of boxing and had a vision.
“There is another world outside of Cardiff and Madison Square Garden and we have an obligation to grow the sport of boxing in new areas and regions.
“This event could change boxing forever, because if Saudi Arabia are willing to invest in these fights, you could see a big change in the dynamic of the sport.”
It is proposed the fight, for Ruiz’s three heavyweight world titles, will take place at a purpose-built 12,000-seater open-air arena.
Press conferences in Saudi Arabia, London and New York are due to be held in the first week of September.