Jefferson led LSU to the Southeastern Conference title last year, although the Tigers lost to Alabama in the BCS title game.
"He's an athletic guy who has a strong arm," Bucs coach Greg Schiano said. "We wanted to gauge his development as a quarterback. I thought he made consistent improvement all weekend. There's a lot of upside there, so I think we would like to have a chance to work with him."
Jefferson said he has a lot of work to do in order to be an NFL-caliber signal-caller and is seen as a long shot to make the team's final roster.
"I just want to prove that I'm a very talented player," he said according to the Times. "I played at LSU for a large (number) of games. I had a very strong winning percentage there. ... I'm a competitor and I can be the pro-style quarterback that Tampa Bay wants me to be.
"But I have to do a lot before I can get to that situation. I have to learn. That's what I'll be doing in my time here. I just want to prove that I can be an NFL quarterback."
Schiano said that the team will sign 22 to 29 players in the coming days.