The paper added the brand, known for its Medusa head logo, could be valued at $2 billion.
London-based Kors a year ago snapped up shoemaker Jimmy Choo Plc for about £896 million ($1.2 billion), expanding beyond its namesake brand.
It is unclear whether the Versace family, which has controlled the brand for decades, would remain as minority shareholders in the business or if Donatella Versace would stay on as creative director.
It also cited rumours saying that the buyer could be United States fashion group Michael Kors Holdings or jeweler Tiffany & Co.
The US fashion group has agreed to buy the Italian firm in a deal worth about €1.7bn ($2bn, £1.5bn), Reuters reported.
Italian fashion designer Donatella Versace attends Green Carpet Fashion Awards 2018, in Milan on Sunday.
Versace and Blackstone both declined to comment to Reuters.
French fashion houses including Paris-based Kering (PRTP.PA) were among those holding talks with the Versace family, the sources said, but considered the price too expensive.
Models present creations at the Versace show during Milan Fashion Week Spring 2019 in Milan on Friday.
Blackstone, which had taken a 20 percent stake in Versace in 2014, will fully exit the Italian company.
The group last year returned to a net profit of just under 15 million euros compared with a net loss of 7.9 million euros the previous year.