Vester Flanagan -- Father Is Ex-NFL Player ... Was Drafted By GB Packers

Vester Flanagan -- the man who ambushed and murdered 2 reporters on live TV -- is the son of a former NFL player who was drafted by the legendary Vince Lombardi ... TMZ Sports has learned.

Vester's father is Vester Flanagan Sr. -- a former lineman who was a college football standout at Humboldt State University from 1957 to 1960. In fact, Vester was inducted into the HSU Hall of Fame in 1975.

As far as his pro career, he never really panned out in the pros.

We've tried to contact Flanagan Sr. for comment -- so far, no luck.