Howard Hill was allegedly hired by the Premier League side during the bidding process for the Olympic Stadium, according to The Telegraph. The 57-year-old resigned from accountancy firm PKF in mid-December.
Championship side West Ham United, where Brady is vice-chairman, won the bid for the ground last year.
"On 11 January 2012 a man, 57, was arrested at an address in Cheshire on suspicion of fraud offences and was taken into custody at a Cheshire police station," read a Metropolitan Police statement. "He was later bailed to return in Feb. 2012 pending further inquiries. As part of their inquiries detectives conducted a search of the residential property."
Two other men were arrested in connection with case last November.
Spurs have denied their involvement in any illegal activity.