The source said the girls stayed in Istanbul for two days before travelling to the border.
An Isis source in Istanbul had earlier boasted that the three girls would soon be in a position to join hundreds of its fighters in Syria, where they are waging a campaign of terror against both the local population and Western targets.
He said: "They are in Istanbul and are trying to reach a town on the Turkish border to cross into Syria. There is someone co-ordinating with them. A smuggler. They can't move by themselves."
The three - who are described as "grade A" pupils - left their homes in Tower Hamlets last Wednesday, travelling to Gatwick airport together, where they boarded a Turkish Airlines flight to Istanbul.
To the apparent dismay of Scotland Yard neither Turkish Airlines, nor the UK Border Force reported that the girls were intending to travel unaccompanied to the region, despite it being a well-worn route to Syria. Shamima is thought to have travelled with her 17-year-old sister Aklima's passport.
Commander Richard Walton, of the Met's counter-terrorism command, said: "On this particular occasion we weren't notified that these girls were travelling. If we had been notified then we might have been able to intervene."
MPs have called for an inquiry into the effectiveness of border controls in stopping British youngsters travelling to the region with the intention of joining Isis.
Counter-terror experts estimate 50 young Muslim women and girls have made the journey to Syria.
The girls' MP, Rushanara Ali, who represents Bethnal Green and Bow, said: "We need the Government to look at the arrangements at border control and whether they are appropriate for unaccompanied minors on these routes."
Police questioned the three when a friend travelled to Syria, but they were not kept under watch as they were not thought to be at risk.
However it has emerged that the older sister of one of the girls recently approached East London Mosque over her concerns about her behaviour.
Salman Farsi, spokesman for the mosque, said: "I told her that if you need anything from us just let us know and she said that all they need is our prayers and she started crying."
Farsi said he did not know who or what had persuaded the girls to flee Britain but they had clearly been manipulated.
The Turkish intelligence services are understood to be hunting for the girls, along with local police assisted by the British police and security services, but their task has been made harder by the presence of a network of Isis "representatives" able to hide the three until an opportunity presents itself to travel to the border.
On February 15 Shamima used Twitter to get in touch with 20-year-old Aqsa Mahmood, a woman from Glasgow who joined Isis and married one of its fighters. Mahmood has previously used Twitter to urge British Muslim girls to join her in Syria.