"We'll see how he does this week," Eagles head coach Andy Reid said Wednesday.
Westbrook was knocked unconscious in the Eagles 27-17 win over Washington on Monday night when he took a knee to his head in the first quarter.
The NFL instituted a rule in 2007 that states a player who loses consciousness during the course of a game cannot return to that game.
Westbrook did not practice Wednesday, nor did he do his scheduled weekly press conference.
Reid and Eagles trainer Rick Burkholder both said the star running back was doing better immediately after the game.
"His eyes were clear," Reid said. "He didn't have that hazy look about him."
Burkholder, who ushered Westbrook off the field is taking the one-day-at-a-time approach, but is encouraged by what he has seen.
"He knows everything," Burkholder said. "He knows his brother was on the field. He knows Andy was behind me. He remembers walking off the field, going to the locker room, being on the field in the second half. He remembers all of that.
"Now, we're looking at a headache. Once his headache clears, and it's a mild headache, but it's still a headache. Once that clears we'll get his heart rate up and see how he responds. If he does well there we'll try some football drills."
Burkholder said through the years he has seen players who were knocked unconscious come back and play the following week and players who were not knocked unconscious not able to play the following week.
"Every situation is different," the trainer said. "Some guys take 10 days, some guys take three days."
The Eagles have one less day to get Westbrook back, after playing Monday night.
"That's one of the things I told management after the game," Burkholder said. "We have a short week. That will play into it. But I can't worry about that. I worry about Brian."
If Westbrook can't play, he will be replaced by rookie running back LeSean McCoy, the team's second-round draft pick out of Pitt.
McCoy played in place of Westbrook, who was out with a knee injury against Kansas City in the third game of the season and finished with 84 yards rushing on 20 carries with a touchdown.
That was the Chiefs. This is the Giants.
Westbrook has done well against the Giants, including an 84-yeard punt return for a touchdown in the Eagles' win in 2003. In nine games against New York, he has topped 100 total yards eight times and 100 yards rushing five times. He's also scored 11 touchdowns in those nine games.
The one Giants game Westbrook missed, early in the 2007 season, the Eagles lost and scored just three points.
"You prepare for Westbrook," Giants head coach Tom Coughlin. "He's a great player and he's a guy they rely on tremendously. In key situations, he's going to get the ball."
This week he might not.
"I'm not a doctor and I'm not Brian, so I don't know," Eagles quarterback Donovan McNabb said. "But it's a tough deal. You get a knee to the head like that, it's tough.
"Will there be pressure if Brian can't play, I hope not, but there will be. For [McCoy] it's just a matter of relaxing. It's a different role for him. He just has to see the hole, hit it and hold onto the ball. The same things he did in camp and the preseason."
McCoy, for his part, said he's ready if he has to go.
"There's always a little pressure on you," the rookie back said. "But that's my job to go in and help us out, if Brian can't go."
Looking to bolster their depth at the position, the Eagles signed P.J. Hill off New Orleans' practice squad. Hill, 5-foot-10, 218 pounds, was signed as a rookie free agent by the Saints out of Wisconsin. He carried 26 times for 128 yards, a 4.9 yards per carry average and scored three touchdowns in the preseason. Among the Saints' final cuts, he was signed to the team's practice squad on Sept. 7.
Reid ruled defensive end Victor Abiamiri (knee), wide receiver Kevin Curtis (knee) and linebacker Omar Gaither (foot) out for Sunday's game. Defensive end Darren Howard (ankle), wide receiver DeSean Jackson (foot), and safety Victor Harris (ankle) did not practice Wednesday, but are expected to be ready by Sunday.