Ms Mueller, whose death was confirmed in February, is said to have been kept by Islamic State financier Abu Sayyaf and his wife, Umm Sayyaf.
Ms Mueller was reportedly kept in a room with four Yazidi teenagers, whom she tried to protect from abuse. The girls are said to have regarded Ms Mueller as a "mother figure".
The American aid worker would leave the room when al Baghdadi visited and weep afterwards as she told the Yazidi girls about the sexual abuse she had suffered.
According to a Yazidi teenager, who escaped, but was previously was held with 26-year-old US hostage Ms Mueller, al Baghdadi took the American as his "wife", repeatedly forcing her to have sex when he visited.
"They told us that he married her, and we all understand what that means," Carl Mueller, Kayla's father, told The Associated Press on Friday, which would have been his daughter's 27th birthday. Her death was reported in February.
Her mother, Marsha Mueller, added, "Kayla did not marry this man. He took her to his room and he abused her and she came back crying."
The Islamic State group claimed Mueller was killed in a Jordanian air strike near Raqqah, the group's self-declared capital in Syria. U.S. officials confirmed the death but not the circumstances.
At the time of her death in Febuary, Kayla Mueller's family released a letter she wrote to them from captivity, expressing her faith in God.
