Ngannou, 35, has no fights left on his current UFC deal but as champion he is still contracted with them for another year.
But should he fail to agree an extension it would allow him to become a free agent and pursue his boxing ambitions.
Fury, 33, last fought in October with an epic 11th round stoppage over Deontay Wilder, 36, which rounded out their trilogy in style.
Challenging Ngannou after his three bouts with Wilder would see the Brit facing arguably the two biggest punchers in the world.
But he is keen to have the spectacle fight competed in the smaller 4oz MMA gloves, evening up the playing field.
I will have retired from competitive, championship boxing and I’ll be ready to do the crossover fights completely.
Tyson Fury on fighting Francis Ngannou after Dillian Whyte
Fury said: “We’ve got Francis Ngannou, he’s a big guy, a big dangerous guy.
“I’d love to see, people going on, ‘Oh, it’s not a fair fight in 10-ounce gloves,’ and that’s correct.
“It wouldn’t be a fair fight in 10-ounce gloves because like [Daniel] Cormier said recently, he said Francis Ngannou is a much cruder version of Deontay Wilder, and we all know what happened there.
“So I think if we’re doing four-ounce gloves, he’d have a bit more chance of knocking me out, but then again, I’d have a bit more chance of knocking him out also.
“So it makes for an exciting fight. And I will try to come in at my heaviest for that fight.
“I’ll try to come in over 300 pounds. Just to nail him to the canvas with one solid punch.”