Donatella Versace, the brand's artistic director and vice-president of the group, has called a staff meeting in Milan for Tuesday, according to the Corriere della Sera newspaper.
Celebrity shoemaker Jimmy Choo, luxury jeweller Tiffany & Co and US fashion group Michael Kors Holdings were listed as possible buyers.
The company in its entirety is estimated to be worth some €1.7 billion, the report said.
Versace could not immediately confirm the news to AFP.
Twenty percent of the brand, known for its Medusa head logo, was bought by US private equity group Blackstone in 2014, and the family owns the rest.
The group, founded by designer Gianni Versace in 1978, boasted sales of €686 million in 2016 and turnover is expected to exceed €1 billion in the “short term”, CEO Jonathan Akeroyd said in June.
Photo: Patrick Kovarik/AFP