The Hollywood pair have not yet confirmed that they are officially dating but are apparently keen to adopt an abandoned dog.
A source told Now magazine: "Mila and Ashton have been touring shelters looking for an abandoned dog that needs a loving home.
"They have their hearts set on a big dog - either a golden retriever or a Labrador."
The two stars first met 14 years ago on the set of the sitcom That '70s Show.
The couple have been spotted holding hands in public and were seen kissing at the wrap party for Kutcher's latest film, a biopic of the late Apple boss Steve Jobs.
Another insider said: "Ashton was Mila's first kiss while on That '70s Show, so they've always had a special bond.
"They started dating in the spring, and things have recently become more serious."