Real's home game against Real Sociedad on Sunday was abandoned after a warning was made to a Basque newspaper, and security is one of the key selection criteria for Olympic bids.
"What happened could happen in any city in the world and it would be wrong to use it against Madrid," said Madrid 2012 bid leader Feliciano Mayoral.
The International Olympic Committee is due to send its inspection team to each of the five cities in February and March next year.
Madrid will be the first city the IOC visits, on February 3.
