The seven-time Formula One champion was admitted to the Georges-Pompidou hospital on Monday, according to Le Parisien, which said he was being treated by cardiovascular surgeon Philippe Menasché, described as a “pioneer in cell surgery".
He has not been seen in public since sustaining serious head injuries in a skiing accident in 2013.
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.
The treatment of the former driving ace, whose precise physical and mental state is unknown is shrouded in secrecy. Mr Schumacher's entourage have issued no comment on the report and the hospital has made no statement about his presence or health.
However, Le Parisien cited an unnamed nurse at the hospital as suggesting he may be showing some signs of recovery.
"Yes he is in my service," the nurse was cited as saying. "And I can assure you that he is conscious."
Dr Menasche is best known for performing the world’s first embryonic cell transplant on a patient with heart failure in 2014.
Formula One’s most successful driver was placed in a medically-induced coma for six months after he hit his head on a rock while skiing in Méribel on December 29, 2013 with his then 14-year old son, Mick.
He was moved from Grenoble hospital to Lausanne before being returned home in September 2014. Corinna Schumacher, 50, his wife, has overseen his care ever since.
She has declined to discuss his condition but it has been suggested by old friends he is unable to walk or properly communicate.
Jean Todt, Schumacher’s former team manager at Ferrari and president of the International Automobile Federation, said this summer that he was “very well looked after. He lives with his family. He is continuing to fight (to get better).”
Mr Schumacher won a record 91 grand prix wins and seven world titles. Lewis Hamilton has 81 victories and five world titles to his name. He won his first two titles with Benetton in 1994 and 1995 before five in a row with Ferrari between 2000-2004.