Skelton beat out Kolb for the starting spot in the preseason but went down with the ankle injury in the fourth quarter against Seattle. Kolb came in and directed the Cardinals on the winning touchdown drive in Arizona's 20-16 victory.
Cardinals president Michael Bidwill said in a radio interview Tuesday that Kolb would be the starter, but coach Ken Whisenhunt would not confirm that to be the case.
"We still have time," Whisenhunt said. "It doesn't look great for John (Skelton) being able to play, but Kevin's had a very good week of practice and has played well."
Skelton and Kolb each started two preseason games before Whisenhunt finally named the starter a little more than a week before the season opener.
Kolb hasn't started a game since Arizona hosted San Francisco on Dec. 11. He took a knee to the head on his third play and left with a concussion that wound up ending his season.
Skelton has not talked to the media this week.
If Skelton can't go Sunday, Kolb's backup will be rookie Ryan Lindley, a sixth-round draft pick out of San Diego State. Lindley was inactive against Seattle.
"You don't want to see that happen in Week 1," Lindley said of the injury to Skelton. "It's a rude awakening, but that's why a lot of teams carry three guys and you've got to be ready for something like that."
Information from The Associated Press was used in this report.