According to The Sun, the Aussie singer was spotted on a secret date with the actor at Chateau Marmont restaurant in Hollywood last Thursday.
An eye-witness told the paper the pair shared kisses as they dined at the luxury eatery, adding: “They seemed to be very much a couple.”
HuffPost UK has contacted a representative for Kylie for comment.
Kylie and Olivier dated for five years before splitting in 2007, and he was by her side during her battle with breast cancer.
He went on to marry Hollywood star Halle Berry, who he divorced last year.
Kylie split from fiancé Joshua Sasse back in February - a year after announcing their engagement.
She later admitted she’d ignored advice about the relationship and hadn’t trusted her instincts.
“It’s not been the easiest times of late but that [her split from fiance Joshua Sasse] is a purely personal matter and I have no regrets,’ she told The Sydney Morning Herald in March.
She added: “Hindsight is illuminating but not always what we want to see.
“I wish I had trusted my instincts on some occasions when I didn’t and I wish I had listened to better advice when I didn’t.”