A US official confirms the account of family spokeswoman Emily Lenzner.
It was first reported by London's Independent newspaper. The official was not authorised to be quoted by name.
Mueller was held for a time by Islamic State financier Abu Sayyaf and his wife, Umm Sayyaf.
Al-Baghdadi took Mueller as a "wife," and repeatedly forced her to have sex with him when he visited, her parents Carl and Marsha Mueller were told.