Unified heavyweight champion Joshua and WBC titleholder Fury were filmed chatting briefly last month after crossing paths in Spain.
The Brits are set to meet twice in 2021, though compatriot Whyte could complicate those plans, as he is due a mandatory WBC title shot early next year.
“That [meeting] looked so staged,” Whyte told Sky Sports. “Those two just met at the right time and the right place? And they were just having a casual chat?
“The way they speak on social media – they want to do this to each other. It looks like it was just staged.”
Whyte, who takes on Alexander Povetkin on 22 August, added: “I was just laughing. I was thinking to myself: ‘Look at these two jokers.’
“If I see someone and they’re talking smack about me and saying they are going to do this and do that, then when I see you, have the same energy.
“I’m not going to be standing outside your car window, standing on the sidewalk speaking to you. Come on, man.”
Povetkin flies to Britain this Friday, two weeks out from his clash with Whyte, who admits there could be some awkward moments with the Russian while both stay in the same hotel in Brentwood, Essex, where the fight will be held in promoter Eddie Hearn’s garden.
“It’s not ideal when you have to stay in the same place as your opponent, especially if we’ve got to be in there for two weeks or whatever it is,” Whyte said.
“It’s not ideal really, because you don’t want to be around somebody you’re going to be fighting, for so long.
“A day or two, or whatever; bumping into him here and there is different from being next to someone. You’re thinking: ‘In a couple of days, we’re going to be smashing each other to bits.’”