The Bluebirds are searching for a new assistant for boss Lennie Lawrence after sacking Ian Butterworth, with ex-Wimbledon manager Burton the leading candidate for the position.
However, Burton explained: “I'm flattered that Cardiff City approached me and I have a lot of respect for their manager Lennie Lawrence.
“However Watford wanted me to stay and that's as far as it goes."
Cardiff are now expected to promote reserve team boss Paul Wilkinson to assistant manager.