Kutcher, 34, and Kunis, 28, are yet to confirm that they are dating each other but they are said to be inseparable, reported Sun online.
"They're basically living together. Like any new couple in love, they're pretty much joined at the hip. They've been sneaking around for months but there's only so long you can keep it quiet. They're staying with each other most nights. Mila's practically moved in to Ashton's Hollywood home," a source said.
Kutcher's marriage with Demi Moore broke down last November, following reports that he cheated on her.
Recently, Kunis and Kutcher were caught kissing at the wrap party for his latest film, a biopic of the late Apple boss Steve Jobs at the weekend.
