The 48-year-old pop princess and Prince Andrew, 57, have reportedly been “quietly dating”.
Aussie magazine New Idea claims the two have been an item for “several weeks”.
New Idea alleges the “close friends” got in touch after Kylie’s relationship with fiancé Joshua Sasse ended in February.
A palace source is quoted saying: “At the moment they’re inseparable. Andrew is 100 percent smitten.”
The magazine claims Andrew contacted Kylie, offering his condolences after her break-up with Joshua.
The pair are said to have been ‘inseparable’ since, with Kylie reportedly spending several nights in the past two weeks with Andrew.
Earlier this year, Kylie was presented with the Britain-Australia Society Award for 2016 by Prince Phillip.
INSEPARABLE: Prince Andrew, 57
The Duke of York and Kylie have a string of failed romances.
She has previously been involved with Jason Donovan, Michael Hutchence, Oliver Martinez, Lenny Kravitz and Andres Velencoso.
Andrew was married to Sarah Ferguson from 1986 to 1996. Their daughters are Princess Beatrice, 28, and Princess Eugenie, 27.
Since his divorce Andrew has been linked to businesswoman Ghislaine Maxwell and onetime Playboy model Denise Martell.