According to the New York Post, the Two And A Half Men actor has taken Mila on holiday to a five-star resort on the island's southern peninsula.
Their resort is said to boast of wooden four-poster beds, a sunken indoor bathtub and private pools.
Despite both Kutcher and the Ted actress refusing to confirm or deny their romance, a source told the newspaper that their break together marks that they are ready to go public now things between them are hotting up.
They revealed: "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."
Earlier this week, it was suggested that Ashton is 'smitten' with Mila, but is trying his best not to "humiliate" soon-to-be-ex-wifeDemi Moore with their blossoming romance, with an insider saying he is "very much in love" with Kunis.