"That's the plan," coach Bruce Arians said Wednesday. "We'll see how it goes."
Arians said Winston is "day to day" and has a "little bit of a brace" on the thumb, but he expects the quarterback to throw by the end of the week.
Winston has led the Bucs to three straight wins to improve to 6-7.
"It's getting better every day," Winston said of the thumb. "I'm just taking it day by day. I'm gonna be ready to go as soon as I can."
Winston said he suffered the injury after his hand hit the helmet of Colts defender Al-Quadin Muhammad just before halftime of Sunday's game. The quarterback said he didn't realize something was wrong until he came out for the third quarter and struggled to grip the football.
"I really didn't feel it in the locker room [during halftime] because it was just coming off the 2-minute drive. I ran in there," Winston said. "But when I came out [for the second half] -- I'm not playing catch in the locker room -- when I came out to grab the ball, I was like, 'Oh!'"
Despite struggling to grip the ball, Winston missed just a series before finishing the game. He threw four touchdown passes against the Colts and added a fifth on the ground, but also had three interceptions. He saw a hand specialist Monday, who gave him the green light to continue playing, although there is still swelling and soreness.
Winston's workload is expected to be very limited this week, with a large portion of the reps going to backup Ryan Griffin. In October 2017, Winston saw minimal reps in practice while playing three games with a sprained AC joint in his throwing shoulder before being forced to miss three games.
Winston did practice Wednesday wearing a soft cast. He participated in drills, but unlike Griffin and Chad Kanoff, Winston did not hold a football, nor did he throw during the 30-minute portion of practice that was open to the media.
"I think sometimes it's good to give your arm a rest, but not your brain," Arians said. "So he's out there taking a drop on every play, telling me where the coverage was, where the ball should have gone. So he got a good mental practice [Wednesday] and it might help him physically."
As far as how he's handling the wide array of opinions and speculation about whether or not the Bucs should bring him back next year, Winston said he's only focused on the present.
"It's quite easy, really, when you've got a game every week. I've got an opponent to focus on," Winston said. "It's bigger than me. It's about this team. We've gotta focus on how we're gonna try to beat the Detroit Lions and whoever our opponent is the next week. But right now, it's the Lions, and we've gotta focus on that."