Fiat Chrysler, the Ferrari parent, did not confirm that.
But Italian prime minister Giuseppe Conte said: "I learn with deep regret the latest news regarding the condition of Sergio Marchionne.
"In this moment my thoughts go to his family."
La Gazzetta dello Sport said Marchionne has been in a hospital in Zurich for over three weeks, due to complications following shoulder surgery.
Another source said the 66-year-old may have been suffering lung cancer and is currently in a coma.
La Repubblica claims that an attempt by intensive care doctors to reduce Marchionne's sedation so that he may attempt to breathe on his own was unsuccessful.