Red or Black?, due to be presented by Anthony McPartlin and Declan Donnelly, is the first major UK production from Cowell's Syco company since Britain's Got Talent.
Syco and Red or Black? co-producer ITV Studios had been in talks with Camelot to get involved with the show, but those negotiations have now broken down.
"We're regularly approached by and undertake discussions with third parties about possible concepts and ideas for future National Lottery games," Camelot said in a statement issued to The Guardian.
"These form part of our ongoing strategy to make the National Lottery even more exciting for players, ensuring we continue to grow sales and build on the £25 billion that our players have already raised for good causes.
"We were approached by Syco and worked with them and ITV on the Red or Black? concept. However, after discussions, we didn't reach an agreement on the venture."
Red or Black?, due to be aired live over seven consecutive nights on ITV1 later this year, will involve contestants attempting to win £1m on the spin of a wheel, after competing in a series of 50/50 challenges.
Syco and ITV are still negotiating the details of their co-production agreement, including the key issue of who will take the lead in selling the format around the world.
"As with all of our programmes we will be seeking to deliver maximum value from the brand in collaboration with our production partners," said a spokeswoman for ITV.
"We have a very strong commercial and creative relationship with Syco and we're in the process of conducting standard commercial discussions with them on Red or Black?."
A Syco spokeswoman added: "Syco are having the usual commercial discussions with ITV Studios, which of course involve looking at the complementary skill sets that both companies bring to the table."
Following the end of talks with Camelot, ITV Studios is understood to be in negotiations with another gaming firm about taking on sponsorship of Red or Black?.
> Simon Cowell: 'Red or Black? is a risk'
Watch Ant & Dec and Simon Cowell explain how Red or Black? will work below: