Quade, who played professional baseball with the Pittsburgh Pirates minor league system, is in his fourth year as manager of the Iowa Cubs.
"Under the circumstances, it's not the way you want to arrive somewhere," Quade said Wednesday. "I'm hoping and wishing the best for Chris. I'm going to go up there and see what Dusty Baker and the club needs, and help as much as I can. I have a lot to learn in a short period of time."
Speier was named third base coach in October, 2004. The Sun-Times reported that he was arrested on the 1200 block of North Dearborn Street.
"I don't know all of the details, nor is it any of my business," Quade said of Speier. "I consider myself an organizational guy. When something like this presents itself, you have to do what's best for the club."
In Quade's absence, Cubs Minor League Infield and Bunting Coordinator Bobby Dickerson will manage the Triple-A team. Dickerson previously managed Double-A West Tennessee from 2002-05.
"There's a chance I'll be back here obviously," Quade said. "Bobby managed many years and will do a great job.
"The guys here could probably use a break from me anyway," he said lightheartedly.
Iowa is 48-47 and four games back of first-place Nashville in the Pacific Coast League's American Northern Division.