He will 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. Read More