Another said Mostefaoui died during serious disorder in a jail in Hassakeh, which houses IS prisoners from various countries.
The death and surrounding circumstances have not been officially confirmed.
After being captured last year, the 27-year-old was held in a prison in north-east Syria controlled by the Kurdish-led, US-backed Syrian Democratic Forces.
Last year, the BBC revealed that Mostefaoui was one of several University of Westminster students to have travelled to Syria.
In April 2014, Mostfaoui told his father that he was going to Amsterdam for a few days, leaving with just a small bag, and he then secretly made his way to Syria.
Four years later, he had his British citizenship revoked.
The sources told the BBC that he was one of around 10 men and 30 women from the UK being held by the militia, but he was the first to die in SDF custody.
The prison where he was held is a converted school. When the BBC spoke to him there last October he admitted joining IS.
Meanwhile, the government has refused to allow adult prisoners to return to the UK, saying they should be put on trial in the region.
A government spokesman told the BBC that the Foreign Office had advised against all travel to Syria since 2011.
"Those who chose to leave the UK and fight for, or support, Daesh potentially pose a very serious national security risk."
Ministers have said that, of the estimated 900 people who have left the UK for Syria to join violent Islamist groups, 20 per cent have died, 40 per cent have returned to the UK, and 40 per cent are still in the region.