The Rev. Federico Lombardi told Catholic News Service the church opposes the death penalty and might use diplomatic channels to intervene in Aziz's case.
The 74-year-old former Iraqi official, sentenced to die by hanging for persecuting Shiites, is a Catholic.
In addition to deputy prime minister, Aziz also served as foreign minister under then-President Saddam Hussein.
He traveled to the Vatican in 1998 and met with Pope John Paul II.
Aziz met with the pope again in 2003 as the Vatican attempted to prevent the U.S.-led invasion of Iraq, said Catholic News Service.
Aziz has 30 days to appeal his death sentence.
He is reported in poor health.
Celebrity Families of 2014 [PHOTOS]