Daniel Cormier On Brush With Jon Jones, 'We're Not Friendly'

Daniel Cormier and Jon Jones came face to face in the lobby of an L.A. hotel right before the ESPYs ... but according to DC, the two kept it cordial.

Sources tell us the UFC rivals had a brief conversation -- but it was more civil than friendly. In other words, they acknowledged each other's presence just to be polite.

When we spoke with Cormier about the situation, he downplayed -- "Nothing happened. All my energy is on [my upcoming fight against] Stipe Miocic."

Cormier reiterated about Jones -- "We're not friendly."

Of course, these guys have one hell of a history -- they have one of the nastiest rivalries in pro sports and have talked an insane amount of trash to each other over the years.

At one point, Cormier even mocked Jon's wife for having a "flat ass."

Jones won both UFC fights against Cormier, though his second victory was overturned after Jon tested positive for an illegal substance.

But, Jon recently told TMZ Sports his animosity toward Cormier has been fading -- and claimed he would even shake his hand if the opportunity presented itself.

We're not sure if the two actually shook during Wednesday's run-in -- but DC made it clear he has no desire to have a friendly relationship with Jon.

It seems the two are on a collision course for a 3rd fight ... Cormier told us it's possible -- but he's gotta get through Miocic first.

When we asked if it would a "dream" to end his career with a victory over Jones -- DC laughed and responded, "It was my dream twice."