Vick suffered a concussion in Philadelphia's 35-31 loss to the Falcons in Atlanta on Sunday night and was forced to leave the game in the second half.
Eagles head athletic trainer Rick Burkholder said Vick doesn't have "a whole lot of concussion symptoms," and would undergo further testing, including seeing an independent neurologist in the next day or two.
Instant Debate: Kitna or Kafka?
"Just because he doesn't have symptoms today doesn't mean he won't have symptoms tomorrow," Burkholder said. "You can't predict."
Vick didn't wear a helmet during the morning walk-through and split reps with backup Mike Kafka, NFL Network's Stacey Dales reported. During the team's practice session, the first-team reps were split between Kafka and Vince Young, a source close to the situation told Dales.
"It's hard to give you the future because you have to do things the right way and go through the process," Reid said.
Vick threw for two touchdowns for the Eagles on Sunday, but he couldn't continue after being spun by a Falcons rusher into one of his teammates, right tackle Todd Herremans. He was replaced by Mike Kafka. Vince Young, who was signed to be the backup, has missed the first two games with a hamstring injury. He's close to returning.
"We're pretty fortunate to have three quarterbacks who can play the game," Reid said. "My message to all three of them was: 'Get ready accordingly.'
The Associated Press contributed to this report.