NY Giants Linebacker -- TRIED TO GET ON 'GAME OF THRONES' ... 'But I Can't Crush Faces'

The role of "The Mountain" on "Game of Thrones" was ALMOST played by a New York Giants linebacker ... but Mark Herzlich tells TMZ Sports producers felt his face-crushing skills weren't up to snuff.

The 26-year-old -- who's listed at 6'4" 246 lbs -- was out in NYC yesterday when he told us about his push to get on the hit HBO show.

Mark also told us he's a serious GoT superfan -- he knows every character, follows every story line ... and even "emulates" himself after one of the key badasses on the show.

As for the guy who got the role of "The Mountain" -- he's an Icelandic powerlifter named Hafthor Bjornsson ... who stands 6'9" 419 lbs ... and can bench press 500 lbs.

Oh, and Mark tells TMZ Sports if the guy wants to play in the NFL, he knows just the position.

Check out the clip.