The hospital in Lausanne, Switzerland, has admitted F1 legend Michael Schumacher could be there for the "long haul".
News that the great German had left Grenoble, where he has been in intensive care since his skiing fall in late December, and is no longer in a coma, was met with elation the world over.
But Britain's Telegraph newspaper cited a source close to the Schumacher family - who are otherwise fiercely guarding the former Ferrari and Mercedes driver's privacy - as confirming the 45-year-old is 'drifting in and out of consciousness'.
And Darcy Christen, the Lausanne university hospital's head of media, confirmed that Schumacher's stay "won't be days. It could be for the long haul".
"The transfer doesn't mean that his condition improved markedly in the last few weeks.
"He is still going in and out of consciousness but he is having more moments of consciousness more regularly than in April. He certainly can't talk but there is some degree of communication.
"His doctors and family speak to him but he gets tired very quickly and needs a lot of rest. So this is kept to a minimum," he added.
Italy's La Repubblica newspaper also quoted hospital sources as revealing that Schumacher had been moved from Grenoble to be closer to his home in Switzerland, and because he no longer needs to be in intensive care.
"It will take a few days for him to stabilise completely, after the transfer," the hospital sources reportedly said. "Then the rehabilitation will begin."
The report also said Schumacher's moments of consciousness are brief, but that he is sometimes able to communicate by using his eyes.
"It will be a very long journey, and it is hard to say what will be the outcome," Christen said. "Whatever happens, it will take a lot of patience."
He said Lausanne's neurology department is headed by field leader Professor Richard Frackowiak, and is one of the best-equipped and modern in the world.
"It combines care and research in the best way," said Christen. "There is no better place for Schumacher at this time."