Mention of the 7/7 ringleader's last will and testament was made in a Home Office report on the bombings that left 52 people dead in 2005.
But a Freedom of Information request for the document has been denied, with the Metropolitan Police refusing to allow it to go public.
Khan, the eldest of the four bombers, killed six people and himself when his explosive device went off on a train pulling out of Edgware Road Underground station. A subsequent video of the terrorist surfaced, with Khan attempting to justify his actions, stating "We are at war and I am a soldier".
It is believed that his will likewise indicates that he intended to martyr himself through a terrorist attack. But despite requests, Scotland Yard - who hold the document - has blocked its release. Non-disclosure of a will is unusual, with most documents open to inspection through the Probate Registry.
But in a response to the Mail on Sunday's FoI request, the Metropolitan Police outlined a number of reasons why it thinks the details of Khan's will should be kept secret.
It argued that releasing it might hamper future probes. In its response, a Scotland Yard official wrote: "I find the strongest reason favouring non-disclosure is the consideration of information which could be vital to any subsequent investigation."
The Met added that it could reveal to others how investigations are conducted and that this might enable suspects to conceal information. But in its latest response to the FoI request, Scotland Yard also cited privacy and human rights concerns.
Maurice Frankel, director of the Campaign for Freedom of Information, said the Met's argument in terms of Data Protection did not stand up.
"I do not think that example is legitimate. If that was the full basis for the decision I would not think it was legitimate," he said. Mr Frankel added that the bomber was dead and as such is not covered by provisions in the Data Protection Act. As to others mentioned in the will, their names could be redacted to protect their identities, according to Mr Frankel.