Bowles also expanded the quarterback controversy to four players, saying it's "definitely possible" that Bryce Petty and/or Christian Hackenberg could play before the end of the season.
The coach backed Fitzpatrick after Monday night's 28-3 loss to the Arizona Cardinals, saying, "Fitz will be back next week. ... Fitz is our starter."
Some 18 hours later, Bowles was waffling, which is out of character for him.
"First of all, after the game, it's always going to be status quo because I'm never going to tell the media anything before I meet with my coaches and my GM and the rest of the staff, so everything is status quo until we have our meeting [Tuesday night]," Bowles said.
Fitzpatrick leads the NFL with 11 interceptions and has led the offense to only three touchdowns during the Jets' current four-game losing streak.
Bowles conceded he "revisited" the matter after his postgame news conference. He pulled Fitzpatrick midway through the fourth quarter of the blowout, inserting Smith, whose only series ended with an interception.
"He did show some promise when he was in there," Bowles said of Smith. "He understood the game plan and he did good for that drive he was in there."
Asked directly if Smith could start Sunday against the Baltimore Ravens (3-3), Bowles said, "We have to talk about more than that. There's a possibility every week there will be some changes made, player-wise."
Bowles didn't sound pleased that Smith told ESPN sideline reporter Lisa Salters before the game that he was "getting antsy" to play.
"I don't have any thoughts on backup players saying anything," Bowles said. "They're backups for a reason. If they get a chance to play, they better prove themselves to be worthy of playing regardless of who that person is."
Smith also attracted attention on the sideline by throwing his baseball cap and tossing a cup of ice on the field moments after Fitzpatrick was intercepted at the end of the third quarter. Clearly frustrated, Smith paced the sideline, waiting for his shot, which came shortly after that.
"I don't think anything of it," Bowles said of Smith's sideline behavior.
The Jets are 1-5. Since 1970, only two teams have rallied from a 1-5 start to make the postseason. With no quarterback of the future, the Jets are open to auditioning Petty and Hackenberg.
"It's possible," Bowles said. "We've still got some stages to go before we get to that point, but it's definitely possible."