The 22-year-old has been in a coma since the start of February, when she was discovered unconscious in the bathtub at her home in Atlanta, Georgia.
But during a concert at the weekend, her father Bobby Brown declared: "I can say today, my baby's awake. She is watching me."
Her aunt Tina Brown is also reported to have made the same comment via Facebook, with several websites quoting her saying: "So many messages, sorry can't answer them all right now but I will get to them later. Just allow me this time with my family. Yes,she woke up and is no longer on life support!!!!! God is good!! Thanks for your prayers. Still a process, but she is going to be ok."
No official statements from the family have been released.
Bobbi Kristina – who was the only child of Whitney Houston – was discovered unresponsive in her bathroom by partner Nick Gordon. An ambulance was called and she was taken to a Georgia hospital.
Her family later issued a statement saying: "Bobbi Kristina is fighting for her life and is surrounded by immediate family. As her father already stated, we are asking you to honour our request for privacy during this difficult time."
The late Whitney Houston was found dead in 2012 in a bathtub at her LA hotel.
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