Koetter said Monday the team would like to see Griffin take his first NFL snaps in a regular season game Sunday against Atlanta
Griffin was the Bucs' No. 2 quarterback in Sunday's 27-20 loss to the Dallas Cowboys, but has only played in preseason games.
"The guy's been here for three years," Koetter said. "He's worked his tail off."
Griffin, 29, competed with Ryan Fitzpatrick for the backup job last season, but Griffin ended up missing most of the 2017 season because of injury.
"I think Ryan Griffin is a really good quarterback," Koetter said. "He tears it up in practice every day, but he's never had the chance to prove it in a real game. After it was clear where our season was going to end up, Ryan Fitzpatrick did his job for us this year."
Griffin completed 68 percent of his passes for 518 yards and four touchdowns in four preseason games. He becomes an unrestricted free agent after this season, and Fitzpatrick also become a free agent. So the Bucs want to take a look at what they have.
"He may or may not be back," Koetter said. "That's not for today's topic, but we just would like to see Ryan Griffin get a chance to get into a game if the opportunity presents itself."
--WR DeSean Jackson suffered an Achilles injury on Sunday that might cause him to miss the final game. Sunday's game was Jackson's first after missing the previous three with a thumb injury.
--QB Jameis Winston completed 34 of 48 passes for 336 yards, one touchdown and no interceptions Sunday. He was sacked three times.
--RB Peyton Barber was the team's leading rusher on Sunday, getting 43 yards on 17 carries.
--WR Adam Humphries had a season-high 10 receptions for 79 yards on Sunday.