Officials told the Times that the men have been providing them with valuable information about the remaining ISIS support structure and leadership.
Nicknamed Jihadi John, he was the black-masked figure who posed in videos, speaking with an unmistakably British accent and brandishing a large knife with which he beheaded his captives. A fourth man, Aine Davis, is imprisoned in Turkey on terrorism charges. The men made up a four-person ISIS cell that captured, tortured and beheaded at least 27 hostages including American journalists James Foley and Steven Sotloff, and USA aid worker Peter Kassig.
He is believed to have lived in West London until 2009 when he travelled to Gaza in an aid convoy.
The mother of James Foley, a U.S. journalist who was beheaded by the cell, said she wanted the two men to be jailed for life.
Aine Davis was jailed in Turkey previous year on terrorism charges, after being arrested near Istanbul in 2015.
His younger brother, Mahmoud, followed him to the war zone and was killed fighting for Daesh in Iraq previous year.
Diane Foley, his mother, said she wanted the two men to face trial in the U.S. and life imprisonment.
London-born Alexanda Amon Kotey was wanted by the United Kingdom and U.S. for his alleged role in the torture and murder of British and American captives.
Elsheikh, who had worked as a mechanic in London, is accused of a similar campaign of torture, including the use of waterboarding and conducting mock executions and crucifixions.
The State Department, in imposing sanctions on Kotey previous year, said he likely engaged in executions and torture, including electronic shock and waterboarding, and recruited several British nationals to IS.
Kotey also acted as an IS recruiter and was responsible for recruiting several other British nationals to join the organisation. He traveled to Syria in 2012 and joined Al Qaeda in Syria before shifting his alliances to ISIS.
The families have long hoped to recover the bodies of their loved ones, but ISIS' control of chunks of Syria rendered the task almost impossible. He left two young children in Britain.
Their victims included Mr Haines, a 44-year-old father of two who had been working for a French aid agency when he was kidnapped in Syria in March 2013.
It has always been believed the hostages he beheaded in a series of violent videos were killed outside Raqqa, the IS stronghold in Syria.