Taylor, however, is currently the clear-cut backup to fourth-year quarterback Daniel Jones.
"Yeah, he'll get, as we get going here in terms of preseason games, we'll talk about whatever we think is best," Daboll said. "But I have full confidence in Daniel. And I have full confidence in Tyrod in what his role is. Each day we sit there and evaluate the guys, but will he get a few reps here or there? He might."
While it could open the door for speculation on Taylor potentially replacing Jones, the pecking order is clear at the moment. Jones, who had the fifth-year option in his rookie contract declined earlier this year and is in the final year of his deal, has taken all but one first-team rep this summer. That one came when Taylor replaced Jones when he was having a conversation with Daboll about the previous play.
Jones also worked with the starters in the preseason opener Thursday against the New England Patriots. He went 6-of-10 for 69 yards. Taylor went 13-of-21 passing for 129 yards, with a touchdown pass in the second quarter.
Both the Giants' starting and backup quarterbacks played a quarter.
Daboll insisted that getting Taylor some work with the first-team offense was in no way a reflection on his starting quarterback's training camp or preseason performance, which has been up and down this summer.
"Absolutely not," Daboll said emphatically. "I learned from a pretty good coach a while ago. Usually, he doesn't tell those guys when he throws them in, because that is what the backup job's role is. You have to go in in a split second and prepare as if you're the starter. Fourth play of the game something happens, you're in and you have to be ready to go. I don't think we'll necessarily tell those guys when it will happen."
The Giants need to prepare for the contingency of needing Taylor in a pinch. Jones has missed games because of injury in each of his first three professional seasons. Jones missed the final six games of last season with a neck injury.
Taylor, 33, has starting experience and has looked good this summer. The Giants signed him to a two-year deal worth $11 million this offseason. The idea was to have Taylor as the backup to start the season and as a potential bridge quarterback next year should the organization decide that Jones isn't the long-term answer.
The new regime of Daboll and general manager Joe Schoen made it clear upon their arrival that they were fans of Jones. They were going to move forward with him as the starter and take this year to see if he was their franchise quarterback.
Jones, 25, was the sixth overall pick in the 2019 NFL draft. Owner John Mara said this offseason the Giants had done everything possible to screw him up, including switching offensive coordinators and coaches with regularity. Jones is on his fourth offensive coordinator and third head coach in three years.
The new regime wants to see what Jones really is in regular-season games working in Daboll's offense. They also hope an improved offensive line -- the Giants signed veteran center Jon Feliciano and guard Mark Glowinski in free agency and drafted right tackle Evan Neal seventh overall -- can make for a more confident and less mistake-prone quarterback.
They're going to give Jones time to prove what he can do. A few snaps in the preseason or training camp practice will not change that, even if it will spark conversation that Taylor could eventually take Jones' job.