The BBC has been told by an "official source" that a British man named Siddhartha Dhar is the focus of investigations into the latest propaganda video by the IS group.
The video purports to show the killing of five men IS claimed were spies.
"A lot of people think it is him," the source said, although there has been no official confirmation.
Mr Dhar, also known as Abu Rumaysah, fled Britain in 2014 while on bail.
The father-of-four, from Walthamstow in east London, had been arrested on suspicion of encouraging terrorism, but later travelled to Syria after being bailed.
A London man says that the child shown at the end of the latest IS propaganda video is his grandson. His claim has not been independently verified.
Henry Dare told Britain's Channel 4 News that he recognized the child as Isa, the son of his daughter Khadijah, who has joined the IS group in Syria.
"I can't disown him. He's my grandson. I know him very well," Dare said.
Tribal leaders in Iraq's Anbar province have said that tribal and security forces have mobilized amid an advance by IS militants near the town of Barwana near Haditha, local media report.
Sheikh Naim Kaoud of the Albu Nimr said that IS was attacking Barwana and Haditha from four directions and that large numbers of IS militants had advanced from Mosul, Syria and Hit towards Haditha.
There are reports from Kurdish and Arabic news sources that Iraqi aircraft are targeting IS near Haditha and Barwana.
The British man believed to be the main suspect in the latest IS propaganda video traveled to Syria despite being on bail for alleged terrorism offenses, The Telegraph is reporting.
Siddhartha Dhar, also known as Abu Rumasayah, was arrested in September 2014 on suspicion of belonging to the banned group Al-Muhajiroun.
But hours after being granted police bail, Dhar traveled by bus to Paris and then on to Syria where he joined IS.
France has begun one-year condemnations of the Charlie Hebdo shootings in Paris in which 11 people were killed.
Ali al-Hassi, a spokesman for Libya's Petroleum Facilities Guard (PFG), the armed group ostensibly under the control of the country's Baida-based government, has said that the oil port of Sidra is now safe.
IS militants attacked Sidra, Libya's largest oil terminal, on January 4, but were pushed back.
Al-Hassi also said that reports that IS had taken over the city of Bin Jawad were untrue and that IS were based 40 kilometers west of Sidra.
There are reports of fresh clashes in west of Sidra in Libya between IS militants and fighters from Ibrahim Jadhran's Petroleum Facilities Guard (PFG).
IS launched an offensive against Sidra on January 4 but were pushed back.
IS militants are attacking the Libyan oil terminals Sidra and Ras Lanuf and are reportedly shelling with rockets, according to sources in the Petroleum Facilities Guard (PFG).
Amid reports that IS militants have resumed their attacks on Libya's oil terminals Sidra and Ras Lanuf today, it is worth recalling that the Petroleum Facilities Guard (PFG) -- set up in 2012 to protect Libya's oil installations -- asked Libya's internationally recognized government in August for more weapons to help it combat IS.
Exports of crude oil from Sidra and Ras Lanuf stopped in December 2014 when the state-run National Oil Corp. declared force majeure.
The IS group in Libya is "determined to seize oil fields/facilities in Libya," says the Atlantic Council's Mohamed Eljarh.