Still, sources told ESPN NFL Insider Adam Schefter that Kolb is unlikely to play Sunday.
Kolb did not practice for the second day in a row on Thursday, leaving a strong possibility that backup John Skelton will get the start.
"He's still got a little ways to go but we'll see," Whisenhunt said of Kolb. "It comes down to whether he can push off and run on it, and that's going to be a function of the next couple of days."
The turf toe injury occurred early in last Sunday's 30-27 loss at Baltimore but Kolb stayed in the game. The quarterback was in a walking boot until Wednesday.
"I really am better today, I feel a lot better," he said on Thursday. "There's a lot more movement in it. We had some progress yesterday evening, so everything's in order."
Kolb said he felt better about his chances of playing on Sunday.
"That's about all I can give you, really," he said.
Whisenhunt was asked if Kolb could play if he didn't practice.
"I'd consider it, especially if we needed him in a certain situation but we'll see how he is tomorrow," the coach said. "He's into it and he's been paying attention."
Skelton had lost the backup job to Rich Bartel after he was slowed by a high ankle sprain in the preseason. Skelton was inactive for the first five games of the season but, after the bye week, emerged as the No. 2 quarterback again when the Pittsburgh Steelers came to Arizona.
"If you remember he was the No. 2 coming in and he played well in preseason until he got hurt," Whisenhunt said. "I just had to feel comfortable with where he was from that standpoint. Getting the scout team reps in practice helped and definitely that bye week did help."
Skelton, a fifth-round draft pick out of Fordham in 2010, went 2-2 as a rookie starter late last season.
"Kevin's working to get healthy. He's doing everything he can," Skelton said. "Those things are just frustrating. I've had them before. We'll see what happens later in the week. As of now I'm preparing like I am the starter, but that's the job of any backup quarterback."
St. Louis quarterback Sam Bradford has missed the last two games with a high ankle sprain and has yet to practice this week, leaving the possibility that both teams will be without their starters on Sunday. Backup A.J. Feeley led the Rams to an upset over visiting New Orleans last weekend.
The Cardinals have lost six in a row heading into Sunday's game, which matches the two teams tied for last in the NFC West.
Information from The Associated Press was used in this report.