Another source told AFP that the man had “no judicial record”.
Officials have said the attacker was a Russian born in the republic of Chechnya in 1997.
His mother and father are being held in custody for questioning.
The attacker stabbed a 29-year-old man to death and injured four othersjust before 9pm near Paris’ main opera house the Palais Garnier.
Eyewitnesses have said he shouted “Allahu Akbar (God is greatest)” before the attack.
Police union representative Rocco Contento said officers shot the knifeman as he ran at them shouting: “I will kill you, I will kill you.”
French TV channel BFMTV offered a conflicting report that he was on the ground suffering from cardiac arrest when he was shot by officers.
The news agency Reuters has seen a photo claiming to show the attacker, who is bare-chested, bearded, and wearing black trousers.
It has not been confirmed if the image shows him from the time of the attack.
Islamic State has said it is behind the attack, calling the knifeman one of its “soldiers”.
The French interior minister is to hold an emergency security meeting.
The knife attack happened just before 9pm on Saturday on Rue Mosigny, an area popular with tourists that is filled with restaurants and bars.
French authorities announced they were launching a terrorism investigation two hours after the attack.
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The knife frenzy in Paris on Saturday comes after a string of terror-inspired atrocities in France in recent years.
French President Emmanuel Macron said France has “once again paid the price of blood” after the attack on Rue Mosigny.