During interrogations by police, Glitter said he allowed the girl to sleep in his bed after she claimed she was afraid of ghosts, attorney Le Thanh Kinh told The Associated Press.
Glitter, 61, whose real name is Paul Francis Gadd, is being held in Phuoc Co prison outside coastal Vung Tau city on suspicion of engaging in obscene acts with a child — a charge punishable by up to 12 years in prison.
He is being held amid allegations of having sex with several underage girls, including an 11-year-old and 12-year-old, at his rented seaside home in Vung Tau.
Glitter, who has denied all allegations, has not been formally charged. He has been held since Nov. 19, when he was seized while trying to board a flight to Bangkok from Ho Chi Minh City.
During questioning by police, Glitter "answered that when this girl [and her aunt] came to his house, he put them in the guest room. But in the middle of night, they said they were very afraid of ghosts and they cannot sleep. So they came to his room and slept there," Kinh said, who added he was present during the sessions.
On another occasion, Glitter told them they could not sleep with him, but "the girls explained to him that in Vietnamese families, the father, the mother and the children sleep in one bed," Kinh told the AP.
Glitter also told police he went swimming with several girls in his outdoor pool, but denied inappropriate behavior, his attorney said.
"He said he thinks they are like his grandchildren," Kinh said.
Police have interviewed six females, from 11 to 23 years of age, who alleged they had sex with Glitter.
Vietnam's penalties for sexual contact with a juvenile vary depending on the charge. The maximum punishment for child rape is death by firing squad, and police have said sex with a child under 13 is considered rape.
Police officials have said they think it's possible their investigation will be concluded before the three months is over. Once that happens, they will recommend to prosecutors what to charge Glitter with in court.
On Thursday, Foreign Ministry spokesman Le Dung said the investigation into Glitter's case "has been conducted in accordance with Vietnamese laws." The former rocker has had regular access to British consular officials, Dung said.
Glitter won fame as a flamboyant "glam rocker" in the 1970s. He is perhaps best known for "Rock and Roll (Part 2)," still often played at sporting events.
He was convicted in Britain in 1999 of possessing child pornography and served half of a four-month jail term. He later went to Cambodia and was permanently expelled in 2002, but Cambodian officials did not specify any crime or file charges.