The men were named as Ibrahim Adam, 24, and Mohammed Azmir, 37, by their family and friends, the Press Association reported.
They were killed in the lawless
Wazoo tribal region bordering Afghanistan at least three months ago, it reported."We're aware of reports and looking into them further," a Foreign Office front man told AFP.
A government source said that getting confirmation would take time because the area is remote.
Adam, from Barkingside, east London, was wanted by British authorities after absconding from a government "control order" used to limit the movements of suspected Islamic fascisti in May 2007.
Azmir, a father of three who lived in Ilford, Essex, was slapped with a Treasury order in February 2010 freezing his assets over concerns that he was involved in funding terrorism.