Barring a setback to his shoulder, the plan is for Winston to eventually be back under center in 2017. Doctors have told him to sit out at least two weeks and he will be re-evaluated following Sunday's game at Miami.
But general manager Jason Licht has said Winston could miss an extended period of time. They want the sprained AC joint in his right throwing shoulder to heal as much as possible.
When asked Monday if he believed Winston would play again in 2017, Koetter didn't mince words.
"I do," Koetter said. "From what I know, I do. But again, it was rest him for two weeks, see where he's at. We talked to multiple doctors. That's what the plan is. There's really nothing to add to that right now. I know Jameis is planning on playing again and there's been no discussion between Jason, myself of him not playing again. That would all be something that would have to come up in the future."
The Bucs will start backup Ryan Fitzpatrick Sunday against the Dolphins. Fitzpatrick passed for 187 yards with a touchdown and an interception in a 15-10 win over the Jets Sunday.
But Koetter said he would also like to see Ryan Griffin get his first regular-season NFL action before 2017 is over, although he said the Bucs would not force it.
"Ryan Fitzpatrick will be our starter this week, we know that much because Jameis will be out again this week," Koetter said. "And Ryan Griffin will go into the week as a backup. If the opportunity ever presented itself, it would be good while we have this situation to get Ryan Griffin into a game and he's been doing well in practice. But it would never be just because we want to see him get into a game. It would have to be the right opportunity and we'll have to see if that ever comes up or not."
While Fitzpatrick was pleased with the victory, he said he expects to play better.
"I love 300-yard games," Fitzpatrick said. "But at this point in my career, with where I'm at, the wins are awesome. They're hard to come by. You have years like this where we lost five games in a row and you start to realize with the year I had last year in New York, it's a tough business. It's hard to win in this league. So I'll take them however they come.
"That wasn't my best effort. I can play better than I did today and I don't think it has anything to do with getting comfortable or feeling guys out. I just think it's about me going in there and doing a better job. The one thing, stepping into this role, it's not like I'm stepping into a role and we're going to try to manufacture some things because we don't have talent. There's so much talent on this offense that it's fun to get into this role and have Dirk call the offense and have him really know the guys and for me to be able to step in and do my best."
--Bucs defensive tackle Chris Baker got into a sideline altercation with linebacker Kwon Alexander and defensive end Robert Ayers following a roughing-the-passer penalty that led to a touchdown pass for the Jets' Josh McCown in the fourth quarter Sunday.
Cooler heads prevailed following the game and all is forgiven, Baker said.
"We just wanted to shut them out in the second half and I made that dumb penalty," Baker said. "I didn't think it was a penalty, but I guess we'll see once they turn it in or whatever. Guys are just passionate, we want to win and we got into a little argument just because it was a dumb play, but that's football. We hugged and kissed afterward and were straight ... heat of the moment."
--Tight end Cameron Brate has cooled off after a hot start to the season. He has only two catches for 19 yards in the past two games with no touchdowns. With Mike Evans serving a suspension, head coach Dirk Koetter said the Jets double-teamed Brate when the Bucs got close to the end zone.
"With Mike (Evans) out yesterday, they actually doubled him in the red zone," Koetter said. "Usually Mike is the one who gets doubled in the red zone. We had two or three things we were trying to go to Cam inside the 25 and they doubled him."
NOTES: WR Freddie Martino was released Monday to make room for Mike Evans to come off the suspended list. ... CB Vernon Hargreaves suffered a hamstring injury in Sunday's game and was unable to finish. He will be evaluated Wednesday. ... WR Chris Godwin had five receptions for 68 yards on 10 targets in the first start of his NFL career Sunday. ... K Patrick Murray is 7 of 8 on field-goal tries since joining the team five games ago. His only miss was a 54-yarder. He has made all five of his PATs. ... WR DeSean Jackson is playing his best football in the past three weeks since signing with the Bucs, head coach Dirk Koetter said. Jackson had six catches for 82 yards Sunday.
REPORT CARD VS. JETS
--RUSHING OFFENSE: D -- The Bucs can't run the football. It doesn't matter who does it. They rushed 31 times. That's the good thing. But they averaged under 3 yards per carry again. That's brutal. And it won't get better until they beat teams down the field in the passing game.
--PASSING OFFENSE: C-minus -- Not much was expected of Ryan Fitzpatrick making his first start and not much was delivered. He did get the win. He passed for one touchdown and had one interception. He was only sacked once. Those aren't bad things considering the Bucs were without Mike Evans. Rookie Chris Godwin stepped up.
--PASS DEFENSE: B -- The Bucs were all over Jets QB Josh McCown. He was sacked him six times by six different players. It helps to have the lead. The Bucs entered the game with only six sacks all season. CB Brent Grimes returned and had his third interception of the season.
--RUSH DEFENSE: A -- The Bucs shut down the run for the most part against the Jets. LB Lavonte David had eight tackles, two for losses, and a fumble recovery. The Jets were in second-and-long all day. This was a very good effort against the run as New York averaged under 3 yards per carry.
--SPECIAL TEAMS: A -- K Patrick Murray was perfect on all three field-goal attempts, including a 49-yarder. He is 7 of 8 on the season, with the only miss coming from 54 yards. P Bryan Anger did a nice job flipping field position.
--COACHING: A -- It's not easy to win a game in the NFL with the backup quarterback. The defense played well. Kudos on a team win. The coaches held the players accountable.