The cardinal, 77, said he has spoken with Archbishop Carlo Maria Viganò, the Apostolic Nuncio who represents the Vatican in Washington, D.C., and asked to begin the process to eventually choose his successor. Viganò is also the conduit between American Catholic bishops and Rome.
"It's just not fair to the archdiocese to have someone who may not be able to do the job as it should be done. So I told him, in light of that, it makes sense to begin the process," Cardinal George said.
Viganò will ask Cardinal George and other American cardinals and archbishops for a list of potential successors. The months-long process arrives at three potential names. That list is then sent to Pope Francis, who can either appoint one of them or chose someone else entirely.
Cardinal George had hoped to have a private meeting with the pope during the canonization. However, because that trip has been canceled, he hopes to speak with Pope Francis in person at another time.
Cardinal Geore: ''Good days, bad days'' with chemo
Cardinal George is undergoing chemotherapy treatment and will not be able to rearrange his schedule to travel to Rome later this month for the canonizations of Pope John XXIII and Pope John Paul II, who appointed Cardinal George to the Chicago Archdiocese.
"I had hoped to be there," he said of the canonizations, but considering his health thought the trip would be "very foolish."
The cardinal's health prompted him to consider his position within the Chicago Archdiocese.
"As you have chemo, there are good days and bad days," Cardinal George said. "The fact that my health is uncertain; it's a question of being able to extend your entire energy on what is my responsibility as archbishop of Chicago."
The cardinal was first diagnosed with bladder cancer in 2006. In 2012, it returned to his kidney and liver, leading several rounds of chemotherapy.
Cardinal George began more aggressive chemotherapy treatment in early March after doctors discovered new cancer cells in his kidney.
This second round of chemotherapy led Cardinal George to cancel his trip to Rome. It was interrupted when he spent a week in the hospital with an infection. He does not want a repeat.
"And that's exactly the week, when that would be the case. So, I could go, but they said you're putting yourself in danger of infection - and if that happens over there, the danger could be great indeed," Cardinal George said.
The cardinal has one more treatment in this series of three.
"They've already postponed the second treatment," Cardinal George said. "They want to do chemo on a regular schedule now, a strenuous schedule. At the end of that, they'll do the scans and see what's worked."
He plans to keep his Holy Week commitments.