The court will announce its decision at 9.30am on Wednesday in Canberra.

Pell, 78, was found guilty by a jury of the rape of a 13-year-old choirboy and sexual assault of another at St Patrick's Cathedral in Melbourne in 1996 but Australia's most senior Catholic has always denied any wrongdoing.

If the leave is granted, the jailed cardinal's lawyers will need to lodge a formal appeal.

The Victorian Court of Appeal in August upheld a jury verdict convicting Pell in a 2-1 ruling.

In a 12-page application for special leave to the High Court, Pell's lawyers argue Chief Justice Anne Ferguson and Court of Appeal president Chris Maxwell made two errors in dismissing the earlier appeal.

Bret Walker SC and Ruth Shann say a mistake occurred because Pell was required to prove the offending was impossible, rather than leaving that onus to prosecutors.

Secondly, they argue the judges erred in not finding the jury's verdicts unreasonable, claiming there was reasonable doubt about whether opportunity existed for the crimes to have occurred.

They also claim that changes in law over the decades since the crimes were said to have occurred make it more difficult to test sex assault allegations.

They argue Pell should be acquitted of all charges for a number of reasons including inconsistencies in the complainant's version of events.

But prosecutors argue there is no basis for the appeal, and the Victorian courts did not make an error.

In their submission to the High Court, prosecutors wrote Pell's legal team were asking the court to apply established principles to the facts of the case, which were already carefully and thoroughly explored by the majority of the Court of Appeal.

Pell is serving a six-year jail term and won't be eligible for parole until he has served three years and eight months of his sentence.