The Deal or No Deal host had been lined up to make a return to Saturday night television on the BBC for new gameshow The Bodyguard.
However, Edmonds is said to have exited the project after filming the initial pilot, reports The Sun.
The show would see contestants becoming celebrity bodyguards while taking part in challenges and obstacle courses.
The presenter allegedly did not find the show "exciting" enough, and would only decide to take on another series if it met his standards.
An insider said: "The BBC and producers Endemol were really keen for Noel to do the show.
"But he filmed the pilot on the basis that he would only do a full series if he thought it was amazing, different and exciting — and he didn't feel that."
The source added: "To take on another big show it would need to really blow him away.
"Endemol were disappointed by his decision, but understand his feelings - it is all amicable.
"Noel thinks The Bodyguard will be a success, but just with somebody else at the helm."
A BBC insider said that a decision on the future of the show will be made in the near future.