Schumacher has been hospitalised since Monday (Tuesday NZT) in the hospital's cardio-vascular surgery department.
In 2014, Menasché successfully performed the first embryonic cell transplant on a patient with heart failure.
According to Le Parisien newspaper, Professor Menasche inspected Schumacher twice in Paris over the summer - the first time at the Pitie-Salpetriere hospital and again when he was transferred to the George Pompidou.
Schumacher was taken to the Pompidou hospital in southwest Paris on Monday afternoon, Le Parisien said, without citing its sources.
The report also claims that the former driver's long-time doctor Professor Gerard Saillant is also with him, while other media believe that Schumacher has previously been on several visits to hospitals in Paris since the accident.
Little has been seen or revealed about the seven-time Formula One champion's condition since his skiing accident in the French Alps nearly six years ago.
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Schumacher's condition stabilized after he was placed in a drug-induced coma, from which he later emerged.
Fans revere the determined German and his name was chanted at the Monza circuit last weekend for Ferrari's most successful Formula One driver Schumacher, with his son Mick, who is part of the Ferrari Driver Academy, present.
In January, Schumacher's family released a statement saying he was in "the very best of hands".
"Michael is in the best hands and is well looked after in his house", Todt said.
He said: "I'm always careful with such statements, but it's true".
"Please understand if we are following Michael's wishes and keeping such a sensitive subject as health, as it has always been, in privacy". "I saw the race together with Michael Schumacher at his home in Switzerland", he explained.