"Rabah Tahari has fled to Turkey after falling out with other jihadists over money. He has a lot of enemies," a security source said as quoted by The Telegraph.
Tahari, a Birmingham native also known as Abu Musab, was said to expose his whereabouts after setting up an account with the professional business network website LinkedIn.
"Right now, we're investigating whether they were planning an attack in Istanbul similar to the one in Paris. We suspect there could have been a parallel attack with Paris, on the same day," the newspaper quoted its source as saying.
Tahari, 46, is claimed to be the leader of an Islamist group, Kateeba al-Kawthar, involved in recruiting British fighters known as the "Beatles." It is claimed to boast fighters from 20 countries, including the United Kingdom.
A joint Washington Post and BuzzFeed News investigation identified last week one of the members of the Beatles, 32-year-old Londoner Alexandra Kotey, whose whereabouts are unknown.
Turkish officials were said to capture another Beatles member, Aine Davis, in November.