George Pell could be stripped of his top Order of Australia honour if his bid to overturn convictions for five child sex offences fails.
Lawyers for Pell, who maintains his innocence, have lodged an application for leave to appeal on three grounds, including that the jury verdict was unreasonable.
It is understood if Pell's appeal is rejected in court, the prime minister's office would then ask the Council for the Order of Australia to consider revoking his honour.
The council has the power to recommend the governor-general revoke Pell's 2005 appointment as a Companion of the Order of Australia (AC), the nation's highest honour.
"We are unable to comment on individual cases regarding the consideration of the termination or cancellation of an award in the Order of Australia," a spokesman for the governor-general told AAP.
Prime Minister Scott Morrison said the full legal process of appeals would have to play out before anything could be done.
"I was appalled and shocked, like any Australian would be, to read of those events," he told reporters on Tuesday.
"It shows that no one's above the law in this country, but we do have the law in this country and that law requires a process now to be followed."
He echoed his national apology to victims of child sexual abuse to tell them they were not alone and people believed them.
"To all of you out there who have been the victims of child sexual abuse, know that we're thinking of you, know that people around you who love you and care for you, they want the best for you," he said.
Senators Derryn Hinch and Sarah Hanson-Young have led calls for Pell's honour to be revoked after a jury found Pell guilty of five charges over the 1996 offences against two choirboys.
Revoking Pell's AC would be similar to disgraced entertainer Rolf Harris losing his Officer and Member of the Order of Australia honours after being convicted of indecently assaulting four girls in the UK.
