Police earlier named Boumeddiene and Coulibaly as suspects in Thursday's slaying of a female police officer in the southern suburb of Montrouge.
With Coulibaly dead, and Charlie Hebdo suspects Cherif and Said Kouachi
killed Friday in a separate standoff north of Paris, Boumeddiene is the last prime, publicly identified suspect that police are seeking in connection with France's recent wave of terror attacks.
A Turkish Prime Ministry source told CNN that Boumeddiene entered Turkey on January 2, arriving at the Istanbul airport on a flight from Madrid with a man.
That means she may not have been in France at the time the policewoman was shot on Thursday, as authorities originally believed. Authorities offered no immediate explanation of the discrepancy, but have said she is wanted in connection with a terrorist attack.
During routine screening of arriving passengers, Boumeddiene and her companion were flagged by Turkey's Risk Assessment Center at the airport and a decision was made to maintain surveillance on their movements.
The pair checked into a hotel in Istanbul and engaged in "tourist type" activity for a couple of days. When her name was made public by French investigators after the Paris terror attacks, Turkish authorities alerted their French counterparts to her movements. Turkish agents tracked her to what the official said was her last confirmed location near the Syrian border.
She had a return ticket to Madrid for January 9, but she failed to take her return flight from Istanbul that day, according to an official in the office of Turkey's Prime Minister.
A French source close to the nation's security services said it's believed that Boumeddiene is no longer in France and she is thought to have left for Turkey, "of course to reach Syria."
French authorities have asked Spain to look into the possibility that Boumeddiene transited through Spain en route to Turkey, a Spanish source close to the nation's security services said.
It is not confirmed that she did travel through Spain, but "it is true that we are working on that line of investigation, on that possibility," the source said.
Earlier, French police union spokesman Pascal Disant said Boumeddiene may have left the market siege and eluded capture as hostages were freed. So far, no witness has publicly said she was there.
But Disant said that the Kouachi brothers and Coulibaly were part of the same jihadist groups, and Paris prosecutor Francois Molins indicated Boumedienne and Cherif Kouachi's wife also were well acquainted, saying they exchanged 500 phone calls in 2014.
Armed investigators on Saturday milled around the apartment shared by Coulibaly and Boumeddiene in Fontenay-aux-Roses, south of Paris.
Both of their names were still on a letterbox in the lobby of the building, situated across from a library.
They lived in an apartment above an Indian restaurant for about five years, according to a neighbor who spoke on condition of anonymity. The neighbor said the couple were always polite, and she often saw them drive around the neighborhood together on a scooter.
As far as the neighbor could remember, Boumeddiene always wore a niqab, a veil that some Islamic women wear to cover all of their head and face except for the eyes.
The French newspaper Le Parisien reported that Boumeddiene was one of seven siblings hailing from Villiers-sur-Marne, France. Her mother died in 1994, and at age 8 or 9 she and some of her other siblings were put into foster care when her father struggled to raise them alone, Le Parisien reported.
The paper reported that Boumeddiene "religiously wedded" Coulibaly in 2009. The next year, Coulibaly and Cherif Kouachi were involved in a 2010 attempt to free an Algerian
serving time for a 1995 subway bombing, a Western intelligence source told CNN.
Coulibaly was indicted May 22, 2010, and spent time in prison in connection with the prison break plot. Cherif Kouachi was under investigation for the same plot, but there was not enough evidence to indict him, the source said.
Photos published by the French newspaper Le Monde purport to show Boumeddiene in 2010 in a rural setting, wearing a niqab and an abaya -- a loose garment covering the rest of her body -- and holding a weapon that appears to be a crossbow.
Another photo shows her pointing the weapon at the camera, but her face is obscured by the niqab, with only her eyes exposed.
CNN has not independently confirmed the authenticity of the photos.
In one of the photos, Boumeddiene in a niqab is posing nearly cheek to cheek with Coulibaly in what the newspaper called a selfie.
Coulibaly holds a pistol in a firing pose in another photo.
In another, Boumeddiene is kneeling and readies to fire the crossbow-like weapon. In that photo, her face and hands are exposed, but her face can only be seen in profile.