According to Le Parisien newspaper the attacker stabbed a man three times at around 9.15pm on Thursday as he was travelling on Line 7 near the Metro station Riquet in north eastern Paris.
It is not believed the attacker knew his victim, who was helped by witnesses and paramedics before being taken to hospital. His condition is not believed to be life-threatening.
The knifeman fled the scene but just before 11pm a passenger told staff at the Metro station Jacques Bonsergent, not far from Place de la Republique on line 5, that he had been attacked by a man holding a knife. He was not injured in the incident.
Police believe it was the same attacker, according to Le Parisien.
Then at around 12.50am two travellers at nearby Gare de L'Est told security staff they too had been subject to an attempted attack by a man armed with a knife. Again police believe the attacker was the same as the one involved in the first two incidents.
A description of the knifeman was not included in the report.
The map above shows Riquet, furthest to the north, Gare de l'Est in the middle, and Jacques Bonsergent to the south. Photo: GoogleMaps
While France remains on high alert due to the threat of terror attacks there has been no suggestion yet from police that Thursday's reported stabbing and attempted stabbings were motivated by terrorism. Specialist regional transport police have been placed in charge of the investigation, Le Parisien reports.
Prosecutors in Paris have so far not commented on the reports.
A spokesman from Paris transport authority RATP told The Local that they were forced to call out paramedics at around 9.15 to treat an injured passenger at Riquet Metro station. The inured man was taken to hospital by paramedics.
They had no reports on the other two reported incidents.