The hospital has refused to confirm or deny the German's presence, but it has also been reported that Schumacher visited the facility twice earlier in the year.
Menasche is a cardiothoracic surgeon who, with his colleagues, has always been working on using stem cells to fix damaged hearts.
Seven time F1 world champion Michael Schumacher is reportedly being treated in a Paris hospital in secret, according to French newspaper La Parisien.
Schumacher was taken to the Pompidou hospital in southwest Paris on Monday afternoon, Le Parisien said, without citing its sources.
Le Parisien suggests that Schumacher will undergo a procedure involving the injection of stem cells destined to produce a systemic anti-inflammatory action in the body.
Jean Todt said Schumacher is "making progress" in his recovery from devastating head injuries suffered in a skiing accident in 2013. "The treatment should start this Tuesday morning, the patient leaving the hospital in principle Wednesday".
His long-time manager Sabine Kehm did not respond to emailed requests for comment.
After spending six months in a medically induced coma, he was shifted to his home in Switzerland for round-the-clock care, but updates about his condition have been few and far between.
The victor of a record 91 F1 races suffered a near-fatal brain injury in a 2013 skiing accident in the French Alps.
Schumacher won a record 91 Formula One races before retiring in 2012.
On Schumacher's 50th birthday, the family released a statement reassuring his many fans worldwide concerned for his welfare, that he was in "the very best of hands".
"Michael is in the best hands and is well looked after in his house", Todt said. "Please understand if we are following Michael's wishes and keeping such a sensitive subject as health, as it has always been, in privacy", the statement read.