Hussain, who is wanted for questioning in connection with the failed attack on Shepherd's Bush station, is said to have been brought to the attention of the Metropolitan Police by the trustees of Stockwell Mosque, in south London.
The trustees allege the 27-year-old Ethiopian was among a group who were trying to take over the management of the mosque by convincing attendees that it was not being run in accordance with Islamic law, Channel 4 News reported.
The news came as Hussain's lawyer was reported as saying that detectives from Scotland Yard are to fly to Rome to interrogate the suspect over his role in the July 21 bombings, ahead of his extradition hearing, due to be held on 17 August.
They claim they wrote to the deputy commander of the local borough in July 2003, accusing Mr Osman and others of inciting racial hatred, supporting extremist views and harassing management at the mosque.
The trustees claim they wrote that the men were trying to "turn this centre into another Finsbury Park," and attached a diary of their complaints, in which police were said to have been called to the mosque because of the behaviour of Hussain.
Concerns were heightened when extremist Islamic graffiti was found on the walls of the mosque threatening the lives of anyone who misinterpreted the will of Allah.
The trustees said the police did not take their complaints seriously enough, although CCTV cameras were installed after a complaint in July 2003. Eventually, the management succeeded in expelling the men.
A spokesman for the Metropolitan Police refused to comment on correspondence between the mosque and the borough command. But the spokesman stressed that police maintain "regular contact" with mosque representatives in the area and that "prompt action" is taken whenever "any concern is expressed".
* Police have charged three men with failing to disclose information about the whereabouts of a suspect in the failed July 21 attacks. Shadi Sami Abdel Gadir, 22, Omar Almagboul, 20, and Mohamed Kabashi, 23, were charged under the Terrorism Act with withholding information that they "knew or believed might be of material assistance in securing the apprehension, prosecution or conviction" of a suspect. Police did not name the suspect. The three men are due to appear in a London court today. Three other people already face similar charges. Yesterday the wife and sister-in-law of a suspected July 21 attacker appeared on charges of failing to disclose information.