Radical cleric Abu Hamza's wife has been asked by her local authority to move out of the five-bedroom council house she lives in.
Moroccan-born Najat Mostafa is believed to live at the large Shepherd's Bush property in west London with two of the couple's children after reportedly moving there in 1995.
Hammersmith and Fulham Council says that in recent weeks it has corresponded with Mrs Mostafa and asked her to move to a "more appropriate property".
But Hamza's second wife is entitled to refuse the council's request, as there is no time limit on her tenancy agreement.
News of the council's request comes just days after Mrs Mostafa's husband was extradited to the US after years of legal wrangling to face terrorism charges. He will appear in court in New York today for a plea hearing.
A spokesman for Hammersmith and Fulham Council said: "I can confirm that we have corresponded with Mrs Mostafa with regards to her tenancy.
"We believe this home is too big for the number of family members who currently live there and, with over 10,000 people languishing on the borough's housing waiting list, she should move to a more appropriate property."
The spokesman could not confirm the exact value of the property, but said house prices in Hammersmith and Fulham are among the most expensive in Britain.
Hook-handed Hamza first faced an extradition request from the Americans in 2004 and was jailed in the UK in 2006 for seven years for soliciting murder and inciting racial hatred.
The former firebrand imam of Finsbury Park mosque has been charged with 11 counts of criminal conduct related to the taking of 16 hostages in Yemen in 1998, advocating violent jihad in Afghanistan in 2001, and conspiring to establish a jihad training camp in Bly, Oregon, between June 2000 and December 2001.
Last week Hammersmith and Fulham council announced it is ending lifelong council houses tenancies and from April 2013 will only offer fixed-term tenancy agreements of two years or five years.
New tenants will have to show that they have made a contribution to the community and demonstrate a five-year connection to the borough.
The new measures will not affect existing tenants such as Mrs Mostafa.