Tommy Tuberville tells TMZ Sports ... Thursday's NFL draft picks should avoid speaking publicly about politics, saying the rookies should straight-up "talk about what you know about."
The Alabama Senator -- who coached future NFL draft picks for YEARS during his tenure as a college headman -- tells us he wants to see less political chatter from athletes, and more playing.
"Nobody's looking for an outspoken person," Tuberville said on Capitol Hill this week of the advice he'd give to his players if they were heading into Thursday's draft. "We're too divided as it is.