Barrett set a career high with 19.5 sacks in 2019, which led the league.
Placing the tag on the outside linebacker would mean quarterback Jameis Winston, an impending free agent, can't be franchised, Schefter adds.
Barrett signed a one-year contract with Tampa Bay last offseason after spending the first five years of his career with the Denver Broncos. He starred on an improved defensive unit during his first season as a full-time starter.
The 27-year-old previously said he'd be willing to give the Bucs a hometown discount on an extension. He'd likely command a lucrative deal if he were to hit the open market.