Jones recently defeated Davis' team-mate Daniel Cormier, but Jones believes he would try harder than Cormier to bring Jones down to the mat and keep him there.
Speaking to MMA fighting about Cormier's strategy, Davis said: "I'm not sure how much he tried to. He went for a couple takedowns early on and then he just started putting hands on him. I mean, he definitely did wrestle. But at the same time, he kind of got away from it."
He added: "I can get down anybody in the world."
In a different interview, this one with MMA Junkie, Davis also chatted about his ambition to fight Jones.
He said: "I'd rather be the guy that takes him off his throne."