Citing a source, the newspaper said two chartered jets were on standby and the suspects would be handed over to U.S. authorities on the tarmac of a British airport.
"The operation is being overseen by the U.S. Justice Department," the source was quoted as saying. "The cost will be picked up by the U.S."
Alun Jones, a lawyer for Hamza, argued in court in London Wednesday Hamza should not be extradited to the United States for health reasons. Jones said Hamza suffers from depression and short-term memory loss and needs further medical evaluation.
Hamza's defense team blamed his health problems on "unrelentingly harsh" prison conditions, the BBC reported.
Hamza and the other suspects -- Babar Ahmed, Khaled al-Fawwaz, Adel Abdul Bary and Syed Talha Ahsan -- face U.S. charges of planning a terror training camp in the United States and assisting hostage-taking in Yemen.
Hamza, jailed for seven years for soliciting to murder and inciting racial hatred, has been fighting extradition since 2004. Ahmed has been held in a British prison without trial for eight years, accused of fundraising for terrorism through a website. Fawwaz and Bary are accused of being aides to Osama bin Laden. Ahsan is being held for his alleged involvement with a series of terrorist websites.