Urquidy (2-1) earned the loss after giving up five runs on six hits and four walks through three innings. He struck out two.
Miller was sent outright to Triple-A Iowa on Monday.
Peters went 1-for-4 with a two-run homer and a strikeout during Monday's 11-2 loss to Texas.
Steele (elbow) is hoping to start a rehab assignment after throwing two more live bullpen sessions, Taylor McGregor of Marquee Sports Network reports.
Thorpe (elbow) is scheduled for a rehab start with Triple-A Charlotte on Tuesday, James Fegan of the Chicago Sun-Times reports.
Urquidy will start Monday's game against the Rangers at Rate Field, James Fegan of The Chicago Sun-Times reports.
Imanaga did not factor into the decision Sunday, allowing two runs (one earned) on five hits, two walks and a hit-by-pitch over two-plus innings against the Mariners. He struck out four.
Suzuki went 2-for-3 with three runs scored, three walks and a stolen base in Sunday's 19-2 win over the Mariners.
Gausman (hand) is listed as the Cubs' probable starting pitcher for Monday's game against the Diamondbacks at Chase Field.
Newcomb will serve as the White Sox's opener for Sunday's game against the Mets, Brooke Fletcher of Chicago Sports Network reports.
