The Egyptian-born cleric is serving a seven-year prison term in England for inciting his followers to kill non-believers, The Sun reported Monday.
He is wanted in the United States on charges of attempting to set up an al-Qaida training camp in Oregon.
His lawyers argue that extraditing Hamza would violate his human rights.
They also say evidence against him should be blocked because it was gained by torture.
Hamza was arrested at his home in May 2004 under a streamlined Anglo-American extradition treaty.
Extradition proceedings were put on hold until his British trial and appeal process had been completed.