EXCLUSIVE

Liev Schreiber will NOT be playing wrestler Chris Benoit -- who murdered his wife and son in 2007, then committed suicide -- in a biopic about the wrestler's life ... despite reports to the contrary ... Liev's rep tells TMZ.

Rumors swirled that Schreiber had signed on to play Benoit in the film "Crossface" -- which has been in the works since 2011 -- but we're told it just ain't so.

Benoit's story is as tragic as they come ... with the wrestler turning on his wife and 7-year-old son in a violent rage that may have been caused by brain injuries he sustained during his wrestling career.