Drew Rosenhaus, Barrett's agent, told ESPN's Adam Schefter his client has accepted the one-year franchise tender but filed a grievance with the NFL Players Association to be listed as a defensive end instead of linebacker.
ESPN's Jeremy Fowler added that Barrett and the Bucs are still discussing a long-term deal before the July 15 deadline.
Per Over the Cap, the 2020 franchise tag value for defensive ends is $17.788 million and $15.828 million for linebackers.
The Bucs announced March 16 they were using their franchise tag on Barrett after he recorded an NFL-high 19.5 sacks last year.
Per NFL.com's Nick Shook, Barrett lined up as a pass-rusher for 508 out of his 836 total snaps in 2019. That doesn't necessarily mean he was at defensive end, particularly since defensive coordinator Todd Bowles tends to favor a 3-4 scheme.
Last season was Barrett's first year with the Buccaneers. His 19.5 sacks were 5.5 more than he had in the previous five years combined with the Denver Broncos.