There is no reference to Azrael in the Catholic Bible, and he is not considered a canonical figure within Christianity. There is, however, a story in 2 Esdras (disallowed by the Catholic and Protestant Churches, but considered canonical in Eastern Orthodox teachings) which is part of the Apocrypha. 2 Esdras has the story of a scribe and judge named Ezra, also sometimes written “Azra” in different languages. Azra was visited by the Archangel Uriel and given a list of laws and punishments he was to adhere to and enforce as judge over his people.
Azra was later recorded in the Apocrypha as having entered Heaven “without tasting death’s taint”. Depending on various religious views, it could be taken as Ezra ascending to angelic status. This would add the suffix “el” to his name, which denotes a heavenly being (e.g. Michael, Raphael, Uriel). Hence, it would be Ezrael/Azrael. Later books also state a scribe named Salathiel, who was quoted as saying, “I, Salathiel, who is also Ezra”. Again, depending on certain views of Christian spirituality, this could be seen as angelic influence from Ezrael/Azrael on Salathiel, though this view of spirituality is neither confirmed nor denied by the Catholic Church.