Hamza, who was jailed for seven years for soliciting to murder and inciting racial hatred, has been fighting extradition since 2004.
Computer expert Ahmad has been held in a UK prison without trial for eight years after being accused of raising funds for terrorism.
Earlier, the Director of Public Prosecutions refused to consent to the private prosecution of Ahmad.
Keir Starmer QC said the documents provided by British businessman Karl Watkin were "very short, lack any meaningful detail and do not provide any real support for a prosecution".
Mr Watkin, a campaigner against the UK's extradition arrangements with the United States, made the attempt to bring legal proceedings in the UK to avoid "outsourcing the country's criminal justice system" to the US.