A statement issued by his family on Friday hailed "a major step in the right direction' but said the 20-year-old Ecuadorean-American was still in a race against time.
"The medical priority for Juan Manuel now shifts from the lungs to the leg injuries that were sustained more than two weeks ago and have not been addressed since the initial emergency intervention [on] the day of the incident," they said.
"Doctors are in a race against time to perform a pending major surgery in order to minimise risk of irreversible injuries to his right lower extremity but can’t proceed until lungs are ready to withstand a lengthy operation."
Hubert died when his car was hit at speed by Correa's after the French driver crashed into the barriers and returned to the track at Spa's fast Raidillon corner during the Belgian Grand Prix support race on Aug. 31.
He was the first driver fatality at a Formula One race weekend since Ayrton Senna and Roland Ratzenberger were killed at Imola in 1994.
Correa suffered a spinal injury and fractured his legs in the crash. He was transferred from Belgium to a specialised intensive care unit in London on Sept. 3.
Friday's statement said he had been removed from extracorporeal membrane oxygenation support (ECMO) and was conscious but not yet fully awake.
"Doctors report that this will take a few days due to being in induced coma for more than two weeks," they added.
"They have also stated that Juan Manuel is fragile and still vulnerable medically speaking and that he remains in the Intensive Care Unit."
The statement added his condition has been changed from critical to serious.