Corden, who wrote the show with Ruth Jones, explained that he would like to examine what happened to the characters.
"Ruth is my closest and best friend and we miss it," he said on ITV1's This Morning. "And I'm interested to find out what happens to those characters as everyone else.
"We've always said that we'd love the idea of making a special. We talk about it."
However, Corden, who recently welcomed his first child, explained that he does not currently have any plans to make another edition of the comedy as he is so busy.
"Gavin & Stacey can't happen at the moment," he said. "There physically isn't any time. But believe me, no-one is more touched than Ruth and I when people come up to us who love the show so much.
"But people only want to see a good one. What they don't want is a rushed, half-baked special... If we are ever going to do one, it has to be better than those ones."
Earlier this year, Corden revealed that he would love to work with his Gavin & Stacey co-star Mat Horne again, and explained that he would like to make a Christmas special of the show.