Here he is ... the KC Chiefs trainer who helped save a closeted gay NFL player from killing himself, David Price, tells TMZ Sports he was "elated" to find out he had such a positive impact.

The player is ex-offensive lineman Ryan O'Callaghan -- who recently came out publicly on Outsports.com after keeping his sexuality a secret during his entire football career.

O'Callaghan -- who played for the Patriots and the Chiefs -- says he was in a dark place toward the end of his career and was on the verge of suicide ... until Price stepped in.

O'Callaghan says Price simply cared enough to talk to him and realized something was wrong -- and convinced him to get help from a team psychologist. That got the ball rolling for O'Callaghan who says he's now in a MUCH healthier mental state and loves life.

We spoke with Price who says he was unaware how important he was to O'Callaghan until he read the Outsports article this week ... but couldn't be more proud of his former player.

"I was just elated, I mean on Cloud 9 that I had that much impact on somebody's life in a positive way."

Price says helping O'Callaghan was a "no brainer" -- and he's confident other people in the league would have done the same thing.