Urquidy (2-1) earned the loss after giving up five runs on six hits and four walks through three innings. He struck out two.
Peters went 1-for-4 with a two-run homer and a strikeout during Monday's 11-2 loss to Texas.
Ryan (glute) will throw a live bullpen session of one inning Wednesday, Dan Hayes of The Athletic 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.
Newcomb will serve as the White Sox's opener for Sunday's game against the Mets, Brooke Fletcher of Chicago Sports Network reports.
Ryan (glute) completed a 35-pitch bullpen session in St. Paul on Saturday, MLB.com reports.
Ober allowed one run on four hits and three walks while striking out three over five innings in a no-decision versus the Padres on Sunday.
Lee went 1-for-3 with a solo home run in Sunday's 8-1 loss to the Padres.
Taylor (6-2) was charged with a blown save but credited with the win Sunday against the Mets, allowing one run on two hits and two walks in the ninth inning. He struck out two.
