Abu Qatada is launching a fresh bid for freedom at the High Court.
The radical preacher will tomorrow ask two judges for permission to challenge his ongoing detention by Home Secretary Theresa May.
The Special Immigration Appeals Commission (Siac) ruled two months ago his detention was lawful.
Leaving him free during heightened security for the 2012 Olympics would be "exceptionally problematic", a judge said.
Lawyers for Qatada, referred to in legal documents as Omar Mahmoud Othman, are expected to argue that the Home Secretary and Siac are acting unlawfully.
The lawyers are applying for permission to seek judicial review and a writ of habeas corpus freeing him from custody while he fights deportation to Jordan.
His last appeal to the European Court of Human Rights over his removal failed on May 9.
Qatada, who is said to have wide and high-level support among Islamic extremists, was convicted in his absence in Jordan of involvement with terror attacks in 1998 and faces a retrial in his home country.
Mrs May restarted deportation proceedings in April after she received assurances from the Jordanian authorities that evidence obtained by torture would not be used against him.
His legal team say they will take the battle back to the European courts if Siac rules against him at a tribunal hearing fixed for October.
Qatada, who is accused of involvement in several bomb attacks, is being held at high-security Long Lartin Prison in Worcestershire. A judge described him as the late Osama bin Laden's right-hand man in Europe.
He featured in hate sermons found on videos in the flat of one of the September 11 bombers.
Edward Fitzgerald QC, representing Qatada, argued at the Siac hearing in May that it would be "quite wrong" if he had to remain in prison pending his deportation challenge.
But Mr Justice Mitting said: "I'm satisfied that managing the risk posed by the appellant outside a category A prison during (the Olympics) would be exceptionally problematic."
Repeated failed attempts by UK governments over the last 10 years to deport the radical cleric have cost nearly £1 million in legal fees, Government figures show.
No figures have been given for how much Qatada has received in legal aid and some estimates put the cost of keeping him in the UK, either in a high-security jail or closely monitored under strict conditions in the community, along with the legal costs of the fight to deport him, at more than £3 million.
A Home Office statement said: "Qatada is a dangerous man and we are pleased (Siac) agreed with us that he should remain behind bars before he is deported.
"We intend to remove Qatada as quickly as possible. The assurances we have secured from the Jordanian government will allow us to do that."