"American Crime Story" is missing out on the biggest mystery surrounding the O.J. Simpson case -- not who did it (we all know that) ... but whose ass Larry King was tapping while he was covering the trial!
Our photog got King and his wife Shawn leaving Craig’s with famed OJ attorney Robert Shapiro -- who's being played by John Travolta in 'Crime Story.'
But Shawn was more interested in who could play Larry -- he's not actually in the TV series -- but as King points out he covered the trial every day on his CNN show. He suggests Warren Beatty for his role (guy can dream) -- but the fireworks start when Shawn asks who he was dating back then.
Watch ... Larry's loose lips get him in big trouble.
For the record ... it was legend back in the day that King was quite the playa back in '95.