"I think we're pretty close," White, speaking on the "UFC on Fuel TV" show, said of the proposed super-fight between the two champions. "If Georges St-Pierre beats Condit, that could be the next fight."
The fight would probably be contested at a catchweight of 180 pounds, between St-Pierre's 170-pound welterweight rank and Silva's 185-pound middleweight division.
"These guys want to fight each other now," White added.
The fight would probably take place in the giant stadium that is home to the Dallas Cowboys.
Silva and St-Pierre are considered perhaps the top two pound-for-pound MMA fighters in the world.
The 37-year-old Silva (30-4) has not lost in 15 fights in the UFC.
The 31-year-old St-Pierre (22-2) has not fought this year because of a knee injury but was recently given a clean bill of health and is expected to meet Condit, the interim title-holder, later this year.