Bowles will move on with Geno Smith as the starter with the Jets' second-year coach getting ready for training camp this week.
"I think Geno can be a good starter, but he's got to prove it in training camp like everybody else," Bowles told the New York Daily News. "It's not just about the quarterback position. You got to have a team around that position to play ball, but he's been in the system a year. He has a better grasp of it going into training camp and we'll see what he does."
Smith, entering his fourth year in the league, has yet to silence his many detractors. He was the Jets' starter in 2013-14. His record was 11-18 as a starter and interceptions were the issue for Smith, who had 34 picks and 25 touchdowns entering last season.
Bowles said last month that there is no deadline for Fitzpatrick to rejoin the team and regain his starting role. NFL Media's Ian Rapoport reported last week that talks had ground to a halt, and they weren't going to pick up any time soon.
Fitzpatrick was reportedly offered $12 million in the first year of a recent three-year contract proposal from the team. Fitzpatrick called the initial negotiations with the Jets insulting.
Fitzpatrick made $3.25 million last season. He turns 34 in November but had one of his best seasons in the NFL in 2015 with 3.905 passing yards, 31 touchdowns and 15 interceptions, starting all 16 games.
Bowles said he is not feeling the pressure to make the playoffs in 2016. The Jets were 10-6 last season.
"I don't feel any pressure," Bowles told the Daily News. "I do what I always do. I coach football. I've been on good teams when I thought we'd be good ... and we were terrible. I've been on teams when I didn't think we had much talent ... and we were very good. So, as a coach, you just prepare and try to make each game the best game you can. And at the end of the year, when you look up, you want to be standing at the top.
"I wouldn't say it would be a failure (if we missed the playoffs). You have growing pains. You want to make the playoffs. That's our goal. ... Ultimately there's only one team happy at the end of the year. We want to go to the playoffs. I don't know if it's going to be a success or a failure, but we need to get to the playoffs and we need to expand from there.
"We won 10 games last year and it wasn't good enough. So we got to try to get to 11 or 12."