Anas al Libi, who was seized by US special forces on Saturday in the Libyan capital Tripoli, arrived in Britain in the mid-1990s and lived in Manchester after being granted political asylum, reports said.
The 49-year-old was accused by the US of involvement in the 1998 American embassy bombings in east Africa which killed more than 220 people.
Al Libi, also known as Nazih Abdul Hamed al Ruqai, was arrested by the Metropolitan Police the following year but was released and later fled Britain.
Appearing on Sky News, the Home Secretary would not comment specifically on Al Libi, but defended the Government's record on tackling extremism.
Detectives are believed to have found an al Qaeda manual at his home which advised Osama bin Laden's followers on how to execute terror plots.
She said: "When we came into Government we took a look at how we dealt with issues around extremism, we extended the work we do to deal with extremism, we have tightened up in terms of the settlement here in the UK and for example, slightly different, I've excluded more extremist hate preachers than ever before."
Al Libi was on the FBI's Most Wanted list and there was a five million-dollar reward for information relating to his capture.