Daily newspaper Le Parisien reported that the woman was heading home at around 9pm on Friday 23rd December after spending the evening with her boyfriend.
She became frightened when she realised she was being followed and walked quickly to the building where she lives in the rue Saint-Amand in the largely residential 15th arrondissement.
Metro newspaper reported that the man then managed to force his way into her studio apartment.
"The young woman was thrown into her studio where the man raped her," said a source close to the inquiry, reported Metro.
"She couldn't do anything. The man then got out his knife and stabbed her nineteen times, leaving her for dead."
The woman managed to find her way to the building's caretaker who called the emergency services.
She was taken to the Pitié-Salpétrière hospital in southern Paris and was able to tell police what had happened before she fell into a coma.
"This could very well be a serial rapist," said the same source. "The police have found elements that establish a link between several crimes committed in the capital where the culprits have still not been identified."
Police are studying video surveillance footage from cameras along the route the young woman took on her way home.