Siddhartha Dhar, also known as Abu Rumaysah, had skipped bail and fled Britain in 2014 with his wife and their four children to join ISIS in Syria.
Born a Hindu, the 32-year-old ran a business renting out bouncy castles in London before converting to Islam and joining the radical Islamist group Al Muhajiroun.
An official source told the BBC that Dhar is the focus of investigations into the video, which purports to show the killing of five men ISIS says were spying for the UK.
"I heard the voice, yes, but I don't know, I'm not sure of the voice. These are the most difficult questions to answer. I just cannot say. I'm not sure within myself whether it is the truth or not," his mother Sobita Dhar told 'The Daily Telegraph'.
His sister, Konika Dhar, from north London, said: "I believed the audio to resemble, from what I remember, the voice of my brother but having viewed the short clip in detail, I wasn't entirely convinced which put me at ease.
She said her brother had converted to Islam more than 10 years ago and her memories of him are from when they were children and teenagers.
"He was a very pleasant boy, and I know it may be hard to believe but he still is, and I still believe that he still can be that person," she added.
One of Dhar's former business associates told the BBC he had "no doubt" the voice on the video was that of Dhar, whohad been arrested on suspicion of encouraging terrorism by the British police but was later able to travel to Syria after being bailed.
In the months leading up to his arrest Dhar was accused of calling for the imposition of Sharia law in Britain.
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