In a written statement, the Italian Interior Ministry said Rome usually grants political asylum in similar cases.
The convert, Abdul Rahman, was released from a prison near Kabul after a court dropped apostasy charges against him due to a lack of evidence and suggestions that he might be suffering from a mental illness.
Afghan officials on March 28 said that he is now at a "safe" location.
Rahman's release has drawn criticism from some Afghan conservatives, who argue he should be put on trial and sentenced to death for violating Islamic law.
(compiled from agency reports)