West Ham, relegated from the Premier League at the end of last season, was awarded the right last February to move to the new stadium in East London after the 2012 games, beating city rivals Tottenham in the process.
A report in the Sunday Times claimed that secret payments had been made to an executive on the Olympic Park Legacy Company (OPLC), the body which unanimously made the decision, during the selection process.
"The suggestion of 'secret cash' in the Sunday Times article is absolutely and categorically denied," West Ham said in a statement on its website.
"As such, legal action is being taken against the Sunday Times, as well as Tottenham Hotspur."
The paper said the executive, Dionne Knight, had been paid 20,000 pounds before and after the decision was made. West Ham said Knight's work was in relation to the procurement of a construction partner after the Olympics.
"This individual had no involvement whatsoever in our stadium process," the OPLC said.
"The individual concerned had declared a personal relationship with an employee of West Ham United FC when she joined the organisation and we therefore put robust measures in place to ensure our Stadium process was not compromised."
West Ham said it was certain of the "robustness" of its bid.
"The OPLC has confirmed that Ms Knight had absolutely no involvement in the bidding process and we repeat that secret cash was not paid to her," its statement said.
"Her work was very transparent and the bidding process was never compromised."
