Members of Sheik Omar Abdel Rahman's family urged Egyptian Foreign Minister Kamel Amr to appear before the country's Parliament to explain why he has not requested the sheik be released, al Ahram reported.
The family members have suggested his release come as part of a prisoner exchange in which U.S. employees of non-governmental organizations detained in Egypt also would be released.
Abdel Rahman was sentenced to life in prison for his role in planning the 1993 World Trade Center attack, which killed six people and injured more than 1,000.
Al Ahram said he is viewed as the spiritual leader of al-Jamaa al-Islamiya, which was behind violence across Egypt in the 1990s, including the 1997 Luxor temple attack that killed 62 people. The group, which has since renounced violence, now has 13 members in the newly elected Egyptian Parliament.
The United States warned Egypt last week it could lose about $1.4 billion in U.S. aid after the country said it's trying 19 Americans working for non-profits in Egypt.
The Americans, among 43 foreign workers charged with spending money from organizations operating in Egypt without a license, include Sam LaHood, the son of Secretary of Transportation Ray LaHood, The Washington Post has reported.
Sam LaHood heads the Egypt office of the International Republican Institute.