"Me and Alex so want kids – well, we are trying, so let's hope, let's hope," she told the U.K. TV show GMTV on Tuesday, a week after marrying Reid during a whirlwind trip to Las Vegas.
Price, a tabloid fixture who used the stage name Jordan, would now like to be known by a third name, too. "Absolutely, Mrs. Reid, yep," she said. "I am in such a happy place, it's so great. You know, new year, new beginning and a new family life to start."
Price, 31, and Reid, 34, are already dealing with speculation that their marriage is in trouble, and she dismissed the notion that the Vegas wedding was part of a media deal.
"The reason we got married in Vegas is because you can't get married anywhere else unless you've been divorced for a certain amount of days," she said. "There was no Elvis or – you know, it wasn't tacky at all. In fact, the pictures are absolutely gorgeous."
Price split last year from her previous husband, Australian singer Peter Andre, with whom she starred in the E! series Katie and Peter. They have two children together. Price also has a third child with another man.