Denise, who has four-year-old daughter Betsy with ex-husband Lee Mead, said she decided not to take up the offer because she didn't want to open up about her personal life.
She told The Sun: "I love the show, but for me it just doesn't work because I've worked so hard to make my situation with Lee work.
"It wouldn't feel respectful to talk about him and our daughter on national TV."
Denise and Lee split in July 2013 after four years of marriage. The pair, who met on the BBC show Any Dream Will Do in 2007, said at the time they would "remain the best of friends", with their daughter Betsy remaining their number one priority.
Denise became a household name in the UK after co-hosting The Big Breakfast in 1997. She is also a West End star having performed as Roxie Hart in Chicago.
However, she said that since turning 40, she has found herself receiving fewer presenting offers. "As you get older there are fewer opportunities," she said. "I was very much the face of the Nineties."
Elsewhere, Denise made her guest appearance in EastEnders this month as sassy businesswoman Karin Smart, and viewers will see the character return to Albert Square next week.
Denise, who provides the voiceover for The Only Way Is Essex, told the newspaper that acting is now her passion.
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