Police investigating the 21 July attempted bombings were staking out a block of flats in Scotia Road, south London, as a result of a piece of evidence they picked up at the scene of one of the attempted bombings.
Leaked documents, said to be part of the independent investigation into the shooting of Mr Menezes by police, suggest they found a gym membership card linked to one of the suspects - Hussain Osman - at the scene of the attempted Shepherd's Bush bombing.
A resident, Abdi Omar, who lives on the floor above Mr Menezes' flat, has since claimed that he had lent his card to Hussain.
At around 0930, Mr Menezes emerged from the block. In a statement to the inquiry, one of the police surveillance team who was trying to identify the suspect from photographs reportedly said he "thought it would be worth someone else having a look".
But the officer was unable to record the man on video because he was "relieving" himself at the time.