PARIS (AFP/REUTERS) - Hayat Boumeddiene, the wanted partner of one of the gunmen shot dead by police after three days of high drama in France, arrived in Turkey before the killings and may now be in Syria, a Turkish security source told AFP Saturday.

"She entered Turkey on January 2," the source said, adding that Boumeddiene had a return ticket from Madrid to Istanbul.

A Reuters source familiar with the situation also said that Boumeddiene left France last week and travelled to Syria via Turkey, and Reuters said that a senior Turkish official had corroborated that account, saying she passed through Istanbul on Jan 2.

The AFP source said she was believed to have moved on to the southeastern Turkish city of Sanliurfa and then to Syria but there was "no concrete data" to prove this. The source said Turkey did not arrest her because of a lack of timely intelligence from France.

"We do not have the luxury to prevent everyone entering without intelligence sharing," said the AFP source, who asked not to be named.

"If the intelligence sharing had been timely then she could have been extradited."

But the source added that the intelligence sharing between the two sides has since intensified and was now "better than normal."

The official's remarks confirm that Boumeddiene was already outside France when the killing spree began, contrary to earlier speculation she had been involved in the Paris killings.

French police had initially suspected the 26-year-old may have had a role in her partner Amedy Coulibaly's acts of violence when he shot dead a policewoman on Thursday and took people hostage in a Paris siege on Friday.

But French police sources said earlier Saturday she was likely already in Turkey at the time of the attacks.

Her arrival in Turkey on Jan 2 also means she was already out of France on Wednesday when two other gunmen slaughtered 12 people at the office of French satirical weekly Charlie Hebdo, kicking off the three traumatic days of violence in France.

Turkey has come under repeated pressure in recent months to tighten its borders to stop Islamists seeking to join Islamic State militants in neighbouring Syria.

But Ankara has insisted it is now doing all it can to ensure full border security and has repeatedly said the West also has a responsibility to share intelligence.