Quoting a statement from the Roman Catholic Archdiocese of Chicago, the Chicago Sun-Times reported George, 69, is recovering from a July 27 operation to remove his cancerous bladder and prostate in the intensive care unit at Loyola University Medical Center.
His doctors don't believe the cancer has spread beyond those organs, the report said.
"There is no evidence of any further gastrointestinal bleeding. Blood counts and vital signs are stable," the statement said. "There is no fever. Although he has episodes of discomfort, the cardinal remains in good spirits and is truly anxious to be feeling better and resume more active rehabilitation."
George's doctors are eager to get him up and moving because the cardinal is a polio survivor, the report said.
Notable deaths of 2014 [PHOTOS]