The former continued his impressive season over the weekend, passing for 315 yards and three touchdowns during Sunday's 31-10 win over the Chicago Bears.
Wilson has struggled for form in recent weeks and passed for just 77 yards during a 10-3 loss to the New England Patriots, leading to his demotion in favour of White.
But, despite those setbacks, there is still a path back into the side for the 2021 number two overall pick, with Saleh unwilling to commit to one player or the other.
"It's a week-to-week deal," he stated. "The full intent is to get Zach ready to play football again. I'll make that decision when I'm ready.
"While we're going through this process, it's Mike White's opportunity to take advantage of every last play he gets. I'm going to leave it at that. We're going to figure it out as we go."
Saleh refused to suggest what White might be able to do in order to secure the starting spot on a fill-time basis, continuing to publicly back Wilson.
"Mike's got an opportunity to stack another great day up this week," he added. "When we feel like Zach is ready to roll, he's going to roll."