EXCLUSIVE

Indianapolis Colts running back Trent Richardson has something in common with Kim Kardashian -- 'cause someone's trying to cash in on a sex tape featuring the NFL star ... TMZ Sports has learned.

We know ... someone is shopping explicit footage showing the former 1st round NFL Draft pick engaged in an orgy with at least 3 women.

The person who has the footage has already contacted various media outlets, including TMZ Sports ... but so far, no takers. We've seen the footage -- let's just say Trent's got a lot in common with the Colts mascot, if you catch our drift.