Having destroyed him in their fight in February 2020, when he scored a seventh round TKO, Fury will look to put Wilder away again in Las Vegas on July 24.
He still wants that lucrative fight with Joshua after Wilder, but claims his next move after that will be to lock horns with Ngannou in the Octagon.
Fury, who is a playable fighter in EA Sports' UFC 4 game, has trained in MMA with Darren Till and Nick Diaz in the past.
"[Diaz] told me Ngannou can't do wrestling anyway so we're just looking for a stand-up bang out," Fury told TMZ.
"Me and Ngannou in the small gloves, make it happen. As soon as I'm done with Wilder and Joshua I will fight Ngannou in an octagon with 4oz gloves.
"He's not a wrestler anyway, it's a stand-up fight."
Ngannou usurped Stipe Miocic to become king of UFC's heavyweight division, beating the long-running title holder at UFC 260 with a vintage striking sequence and subsequent knockout.
He still has plenty of unfinished business in the MMA world but 'The Predator' has already expressed an interest in taking on Fury in the squared circle.
"I don't want to fight Mike Tyson but I would like to fight another heavyweight boxer such as Tyson Fury," Ngannou said, as per The Mirror.
"Absolutely. I'm open to that. Remember boxing was my primary dream and I still have the fire, the dream inside me and I believe at some point, I'm gonna make a step."
Ngannou's unrivalled power has seen him blow opponents away in the Octagon but his striking coach Dewey Cooper reckons the Cameroonian has the skill-set to make the switch to the squared circle and even beat Fury.
"Tyson Fury is difficult for any heavyweight because of the attributes, the speed, the boxing ability, the good defense, the confidence, the swagger of Tyson Fury. Tyson's a real one," he told RT Sport.
"Tyson's a tough fight for anyone in boxing, but Francis definitely could fight any heavyweight, with time and amending the training a little bit.
"He could definitely do it because Francis does have power, however, with a boxing glove the power will decrease a little bit compared to what it is with an MMA glove because an MMA glove is only four ounces when a boxing glove is 10 ounces. So that makes a difference, you know, a lot of little intangible things.
"But to answer your question, of course he can box and of course he could eventually beat someone like a Tyson Fury, for sure. It just, you need to go into a straight boxing format."
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