Parker said they had a "funny and relatable" script but things did not move forward.
"It's over... we're not doing it," Parker told Extra.
The actor famously played Bradshaw on the HBO hit that ran from 1998 to 2004 and reprised it on the big screen in 2008 and 2010.
"I'm disappointed. We had this beautiful, funny, heartbreaking, joyful, very relatable script and story. It's not just disappointing that we dont get to tell the story and have that experience, but more so for that audience that has been so vocal in wanting another movie."
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But Cattrall, in a tweet, slammed the report, saying she had made it clear in 2016 that she did not want to do a third movie.
"The only 'DEMAND' I ever made was that I didn't want to do a 3rd film," she tweeted.
Actor Kristin Davis, who played Charlotte in the hit series, however, said it was "deeply frustrating" to not be able to make the movie.
"It is true that we are not going to be able to make a 3rd film. I wish that we could have made the final chapter, on our own terms, to complete the stories of our characters.
"So we will just have our memories, but please know that all of the love and support for us through the years is felt by us and we are so grateful for all of you! SATC forever in our hearts."
"SATC" also featured Cynthia Nixon.