Tynes injured the left ankle on a kickoff during special teams drills. He walked off the field under his own power and was later sent to the locker room.
Tynes, who is 5-of-8 in field goals and is perfect on 13 extra-point tries, is listed as questionable.
The Giants also could use rookie punter Matt Dodge on kickoffs, considering his experience there at East Carolina. But it is unlikely they would trust the punter with field-goal duties.
"Dodge has done that. He's kicked off," Coughlin said. "We have some flexibility there."
Dodge kicked off 137 times during his three-year college career but had just 10 touchbacks.
"At times, I thought I was pretty good at it, for sure," Dodge said. "I had a few touchbacks here or there. We sprayed the ball around a lot. I feel I could do it if I needed to."
Dodge said he also hit an extra point and attempted a field goal in college, though he did miss the 40-plus-yard field goal.
"I pulled it," he said.
Dodge did some kickoff work Friday after Tynes came off, but it was not extensive.
"It was kind of like an extended warm-up," Dodge said. "It wasn't intense. Just something to make sure I could do it."
But Dodge was reluctant to pencil himself in anywhere but punter after seeing how Tynes entered the locker room.
"He doesn't look like he's hobbling at all, so encouraging," Dodge said. "I think he will be OK."
Notes: C Shaun O'Hara, who has missed the past three games with Achilles and ankle issues, took snaps with the first unit, but remained questionable. "He felt good about it," Coughlin said. "He's making progress. I'm sure he'll be a gametime decision." ... WR Victor Cruz (hamstring), FB Madison Hedgecock (hamstring), DE Mathias Kiwanuka (neck) and DB Brian Jackson (neck) remained on the stationary bikes and were ruled out for Sunday, as was T Will Beatty (foot). ... LB Keith Bulluck (toe) continued to work and appears to be on track to return Sunday after missing two games, though he is listed as questionable. ... RB Danny Ware (groin) is also questionable.