Wilson said he jammed his index finger then had trouble gripping the ball in Saturday's game.
He threw two interceptions and completed just 3 of 9 passes for 15 yards and a touchdown before he was replaced by Adam Schulz.
Schulz and freshman Conner Manning both got more reps in Tuesday's practice, but Whittingham said Manning would only play in a "disaster" scenario since the Utes want to redshirt him, Whittingham said.
Wilson admitted his hand was sore following Tuesday's practice, but he wants to play.
He wore a glove on Tuesday and may wear one on Saturday to help protect the finger and several cuts he suffered on the hand against UCLA and Stanford.
"I'm going to suck it up and play and do the best I can for this team," he said.
The Utah Utes have explained away all their issues on third downs, so now they are left with this notion they're just bad on them, on both sides of the ball.
Whittingham acknowledged as such following Utah's loss to Arizona in which the Utes were only 5 of 18 on third-down conversions while Arizona was 12 of 20.
For the season, the Utes are a miserable 32 of 100 while their opponents are 51 of 123.
Only 17 out of 123 schools are more futile in third-down production than the Utes. The good news for the Utes is one of those teams is USC, which has converted on just 26 of its 90 third-down plays.
Still, that isn't much consolation for the Utes.
"We're bad on both sides of the ball," Whittingham admitted. "It's not just offensively. It's stopping third down, defensively."
The kicking game could be interesting for both teams on Saturday with Andy Phillips having missed two field goals against the Wildcats, his first failed attempts after he started the season 11 for 11.
Phillips did make one from 44 yards out to go into the USC game 12 of 14 on the season.
Whittingham expressed confidence the kicker could find his mojo again this weekend.
"Andy's a tough kid and it's unfortunate we missed those two kicks, but if you would have told me at the beginning of the year, he's going to make 12 of his first 14 kicks, I think we all would have taken that," he said.
Meanwhile, USC kicker Andre Heidari is having his own issues. He made a 22-yarder against Notre Dame, but missed from 40 and 46 yards and is just 6 for 11 this year.