Donatella Versace, Gianni's sister and the company's artistic director, has reportedly called a staff meeting on Tuesday.
Versace, known for its bold and glamorous designs and its Medusa head logo, is one of a clutch of family-owned Italian brands cited as attractive targets at a time when the luxury industry is riding high on strong demand from China.
"We believe that the North America retail environment remains highly promotional, which is impacting the long-term brand equity of Michael Kors", Chief Executive John Idol told analysts in 2016, according to a FactSet transcript.
Shares in Michael Kors fell in early USA trade and were down 8.7 percent by 1526 GMT.
A representative for Versace declined to comment on the potential transaction.
Private equity group Blackstone bought a 20% stake in Versace in 2014, valuing the company at $1 billion, to fund overseas expansion with the idea of taking the company public.
Michael Kors Holdings Ltd.is adding some Italian flair.
French fashion houses including Paris-based Kering were among those holding talks with the Versace family, the sources said, but considered the price too expensive.
London-based Kors previous year snapped up shoemaker Jimmy Choo Plc for about 896 million pounds ($1.2 billion), expanding beyond its namesake brand. Silas Chou and Lawrence Stroll, former investors in the Kors business, are not involved in this deal, sources said.
Two of the three sources who spoke to Reuters said the company had agreed to pay a large premium for Versace. A spokesman for Blackstone had no comment.
She holds a 20 per cent stake in the company, her daughter Allegra has a 50 per cent stake, while Santo, Donatella's brother, holds the remaining 30 per cent.
Versace was founded by Gianni Versace in 1978.
Models present creations at the Versace show during Milan Fashion Week Spring 2019 in Milan on Friday. The 40-year-old fashion house returned to profit in 2017 and reported revenue of almost $800 million.