"It's been going on for around six weeks," an insider said. "They are really happy. They have actually known each other a while through mutual friends and would sometimes bump into one another at industry events, but it has only just turned into something more."
Davis, 47, is best known for her work in the "Sex and the City" TV and film franchise.
Sorkin, 50, is co-creator of "The West Wing" and writer of the film "The Social Network."