|Mila Kunis and Ashton Kutcher|
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."
Mila and Ashton first met 14 years ago when they co-starred in hit sitcom 'That 70s Show', and the pair have recently rekindled their spark.
They are said to be inseparable and "basically living together", so sharing custody of their new pet shouldn't be a problem.
'Two and a Half Men' actor Ashton - who is currently in the middle of divorce proceedings with Demi Moore - whisked Mila off on a luxury five-star holiday on the island of Bali in August.
Though they haven't confirmed their romance, the couple have been spotted holding hands in public and were caught kissing at the wrap party for Ashton's latest film, a biopic of the late Apple boss, Steve Jobs.
A source 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."