Matt Lauer -- Hunt Is On For 1st Ray Rice Interview

Matt Lauer knows ... the first morning show to interview Ray Rice WINS -- and that's why the "Today" show ... and everyone else in morning TV is officially in on the chase to lock down the NFL star.

Matt played coy when we asked if he had already reached out to Rice -- but the answer was written all over his face.

He also explained, "Ray Rice has a story to tell that he wants to get out there." It's clear, Lauer wants to be the one to help him tell that story.

"I think anybody who does what I do for a living would wanna sit down with either of them [Ray and Roger Goodell] and Janay as well."

Ray has texted back and forth with some ESPN reporters over the past few days -- but it's unclear if he's committed to an on-camera interview ... yet.