Under a court order, Children's Hospital of Oakland in California is allowed to remove Jahi McMath from a ventilator at 5pm local time (1am on Tuesday, GMT).
But her family believes the girl is alive and is hoping to be able to move her to another facility where she can be kept on a breathing machine.
Jahi went into cardiac arrest earlier this month. Pic: KPIX/CBS
The battle is dividing public opinion in the US.
Jahi suffered complications after undergoing a tonsillectomy at the hospital on December 9.
After she awoke from the operation, her family said, she started bleeding heavily and went into cardiac arrest.
Both the hospital and an independent paediatric neurologist from Stanford University have concluded the girl is brain dead.
The family is hoping to move her to a New York facility.
"The family is together, and today everybody is praying and being together," Chris Dolan, the family's lawyer, told the AP news agency.
After two California care homes withdrew offers to accept her, Jahi's family views the New York option as their "last, last hope", said Mr Dolan.
The hospital said it would need to confirm there is "lawful transportation" included in any plan to transfer Jahi, and written permission from the coroner.
