It is a clear sign that Schumacher is making progress after suffering severe head injuries in the 2013 accident.
Mick Schumacher doesn't mind the comparisons with his seven-time F1 champion father Michael.
Le Parisien, citing sources it did not name, said Schumacher has been treated at least twice previously at the Georges-Pompidou hospital, admitted each time under a false name and treated by a small medical team.
After the bad skiing accident, Schumacher's condition stabilised when he was placed in a drug-induced coma.
Le Parisien newspaper reported earlier this week that Schumacher has been in the hospital's cardiovascular surgery department since Monday and is in the care of cardiac surgeon Professor Philippe Menasché, who specialises in cell therapy to treat heart failure. "And I can stutter you that he is acutely conscious".
The newspaper said he was due to receive an anti-inflammatory stem cell perfusion on Tuesday and to leave hospital on Wednesday after being transferred from his house in Gland in Switzerland in an ambulance.
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Schumacher is said to have been subjected to transfusions of inflammation-reducing stem cells, part of Menasche's ongoing care to remedy the devastating head injuries the thrill-seeking F1 champion had sustained some six years ago during his fateful skiing accident.
Fry said: "Corinna (Schumacher's wife) and the family have kept very tight control on information about his condition and his treatment which, I think, is a pity".
Schumacher has been recuperating at home in Switzerland since and is visited only by close friends, none of whom have divulged specifics about his state of health.
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Details of Schumacher's treatment have been shrouded in secrecy at the behest of Professor Menasche for propriety reasons and medical confidentiality.
Schumacher's management declined Yahoo Sports' request for comment.
"There are millions of people out there who have a genuine affection for Michael, and that's not just his fans in Germany or fans of Mercedes Benz".
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He is often described as the greatest Formula 1 driver in history, holding several records in the sport including the most world championships, most wins, most fastest laps and the most races won in a single season.