British terror suspect Babar Ahmad has launched a High Court appeal to halt his extradition to the US.
A judge has decided that his judicial review application will be heard with fellow suspects Abu Hamza and Khaled al-Fawwaz on Tuesday.
The judge is also considering a request from a fourth suspect, Adel Abdul Bary.
Last week, the European Court of Human Rights gave its final approval for the extradition of five major terrorism suspects from the UK to the US.
It meant the extradition of the men, wanted for years by the US, was likely to happen within weeks.
Meanwhile, an application by anti-extradition campaigner Karl Watkin to privately prosecute Mr Ahmad and his co-accused Syed Talha Ahsan has been turned down by the Director of Public Prosecutions, Keir Starmer.
In a statement, Mr Starmer said the documents provided by Mr Watkin were "very short, lack any meaningful detail and do not provide any real support for a prosecution".
Mr Ahmad's family had urged Home Secretary Theresa May to halt the extradition until the decision was made.
Mr Watkin said he was calling for a UK trial because the alleged crimes had taken place in the UK and the Crown Prosecution Service had not acted. He said 149,000 people had signed a petition to Parliament about the case.
He said the decision "smacks of a determined effort to extradite both these men" and said their cases were worlds apart from that of convicted terrorist Abu Hamza.
"The public will decry this decision as it supports a trial of British men thousands of miles from Britain, where the alleged crime was committed simply because in the DPP's opinion, the evidence is too weak to prosecute here.
"If that's not outsourcing our criminal justice system, I don't know what is."
Mayor of London Boris Johnson has also restated his support for Mr Ahmad to be put on trial in the UK.
"If there was a crime committed it was committed in this country. There is absolutely no reason why this gentleman should not be produced before the British courts, arraigned and asked to answer to whatever his crimes are here in the UK. British citizens shouldn't automatically be extradited for trial in America for alleged crimes which didn't all take place there."
The last-ditch challenges will be heard by two judges, Sir John Thomas, President of the Queen's Bench Division, and Mr Justice Ouseley.
Hamza and Al-Fawwaz have already been granted interim injunctions preventing their removal pending the hearing.
The defendants will need to prove to the judges that there is "some new and compelling factor" that has not been already considered by previous courts.
Mr Ahmad has been held in a UK prison without trial for eight years after being accused of raising funds for terrorism with his co-accused, Syed Talha Ahsan.
Hamza, who is accused of planning a terror training camp in the US and assisting hostage-taking in Yemen, has been fighting extradition since 2004.
Adel Abdul Bary and Khaled al-Fawwaz are accused of being aides to Osama bin Laden in London.
After the European judges' ruling, the Home Office said Hamza and Mr Ahmad, with Mr Talha Ahsan, Adel Abdul Bary and Mr Al-Fawwaz, would be "handed over to the US authorities as quickly as possible".
Between 1999 and 2006, the men were indicted on various terrorism charges in the US.
The men have argued they would face inhumane treatment in the US.