In January, police found the 22-year old unresponsive in a bathtub inside of her Georgia home.
She has been in a medically induced coma ever since.
Brown is the daughter of singer Whitney Houston, who passed away after also being found unresponsive in a bathtub, in February 2012.
Last month, doctors removed Bobbi Kristina's breathing tube and placed her on a ventilator, indicating she would need breathing support for weeks or even months.
Brown's family said she's been "fighting for her life" since she was found in her bathtub, face-down. A police investigation is ongoing and few details on her condition have been released.
The source did not say where she was moved or provide an update on her condition. She had been hospitalized since Jan. 31 when her partner, Nick Gordon, and a friend found her inside her home in Roswell, Georgia.
Brown turned 22 earlier this month and her aunt released a statement, asking the public "to continue to keep her in your prayers as she is still fighting the battle of her life."
It wasn't the first time police have been called to the townhouse in adjacent Alpharetta, Georgia, where Brown has lived with Gordon. Brown frequently referred to Gordon as her husband, but a lawyer for her father, singer Bobby Brown, said they never married.
On Jan. 23, a security guard at their gated community called 911 reporting a fight at Brown's address. The guard said a neighbor reported people "hitting each other and swinging" outside the townhome. The guard did not describe the people involved, and no one was there when officers arrived.
Police were called to the home on July 8, 2013, and Gordon told officers Brown was unresponsive after falling on the floor. Gordon described it as a seizure, but Brown told police she had no history of medical conditions and had never had a seizure. The incident report says Brown was disoriented and was taken to a hospital.
(Some information from the Associated Press.)