Matt Lauer wanted to sit down with Cleveland rapist Ariel Castro.

Lauer and his crew were turned away from interviewing the monster. 

TMZ reports the NBC crew showed up Friday morning at the Cuyahoga County justice center in Cleveland -- where Castro is being held -- but sheriff's deputies turned him away because the media was persona non grata.

It wasn't Castro's choice -- we're told Lauer's timing was just off.  In fact, sources at the jail tell TMZ ... when Lauer walked in to the jail, he made it seem as if the interview was prearranged -- something to the effect of, "I'm here to interview Ariel Castro."

It's the second time Lauer's been turned away from a major interview -- back in 2011, Lindsay Lohan shut Matt down at her front door.

A rep for the "Today" show declined comment.