Two judges in London will also consider a challenge by a second terror suspect, Khaled Al-Fawwaz, next Tuesday.
The two men are seeking injunctions to stop them being flown to the US.
Pending the hearing by Sir John Thomas, President of the Queen's Bench Division, and Mr Justice Ouseley, interim injunctions have been issued preventing their removal.
The latest legal action comes after Europe's human rights judges this week rejected a bid for an appeal by Hamza and four other terror suspects, paving the way for their extradition.
A panel of five judges threw out their request to the Grand Chamber of the European Court of Human Rights.
Hamza's lawyers have fought a successful campaign to fight his extradition for several years.
His grounds for appeal are not known as this stage, though they could be based on his health. Hamza has also claimed he would be treated unfairly if he were sent to the US.
Hamza was jailed in 2006 for seven years for soliciting to murder and inciting racial hatred.
He is currently charged with 11 counts of criminal conduct related to the taking of 16 hostages in Yemen in 1998, advocating violent jihad in Afghanistan in 2001 and conspiring to establish a jihad training camp in Bly, Oregon, between June 2000 and December 2001.
A Home Office spokesperson said: "The European Court of Human Rights ruled there was no bar to the extradition of these men. We will continue working to ensure they are handed over to the US authorities as soon as possible."
Meanwhile, immigration judges have announced that they will hear radical cleric Abu Qatada's appeal against extradition to Jordan on October 10.
The European Court of Human Rights ruled in May that Qatada's deportation to Jordan could go ahead providing no evidence obtained through torture was used in any impending trial.
The British government has said it has now obtained that assurance from the Jordanian government, which has amended its laws on the use of torture evidence.
Sky News Home Affairs Correspondent Mark White reported that immigration court officials say a substantive hearing for the case will begin on October 10.
Qatada will remain in prison until then.