Jihadi John, real name Mohammed Emwazi, rose to notoriety in a video in August 2014 which showed the beheading of US journalist James Foley.
The 40-year-old had been abducted in Syria in November 2012. His family said they found comfort in being told by fellow captives that Mr Foley had "brought a light to that very dark place and his life brought a light".
Mr Foley's mother said he had a "deep" Christian faith and was working in Syria to uncover stories of the people living in a war zone.
Following his death Pope Francis called his family to offer his condolences.
The terrorist also appeared in videos showing the killings of UK hostages Alan Henning and David Haines, American journalist Steven Sotloff, aid worker Abdul-Rahman Kassig and Japanese journalists Kenji Goto and Haruna Yukawa, also Christians, shortly before they were killed.
A US official told the Associated Press a drone had been used to carry out the attack on a vehicle in Raqqa which was believed to be carrying Emwazi.
A Downing Street spokeswoman said: "We are aware of the US statement about the airstrike targeting Mohammed Emwazi. Like them, we are not commenting further at this stage."
Emwazi's death has not been confirmed but reports suggest Pentagon officials are confident he is dead.
He appeared in the videos dressed in black with only his eves visible, and spoke with a British accent as he went on anti-western rants to the camera while wielding a knife.
It was not until February this year that the jihadist was unmasked as Kuwaiti-born Emwazi, who lived in the UK since the age of six.
He had went to a Church of England primary school in London.
