A spokesman for the couple added: "Their decision to marry has not been made with any pre-conceived commercial plan or media deal in place, and their reason for getting married is purely down to their love for each other."
However, photographers have been following the pair during their stay in Las Vegas.
Price, who sold the picture rights for her wedding to Andre in 2005, used a magazine interview this week to reveal she had plans to marry Reid.
"This year I will marry Alex and I'm going to have his kids," she said.
Speaking on The Chris Moyles Show on Radio 1 on Wednesday morning, Andre said he had "no negative feelings" about the marriage of Price and Reid.
The singer, who has two children with Price, added: "As long as there's a good influence to the kids, I'm happy.
"I don't have any negative feelings inside me. As long as they're happy, great."
Reid, who was booed on the launch night of Celebrity Big Brother, said after he won: "What an amazing, fantastic start to a new year."
When presenter Davina McCall asked him how he had turned the public's perception around, he said: "I'm speechless. My whole agenda in here was just to be myself. I know I'm a good guy."
Asked by McCall: "Who is Alex Reid?", he said: "He's a man, he's passionate, he's going to win a fight in three months. I'm a fighter and I'm a man in love."
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