Gianni Versace was 50 when he was murdered outside his Miami mansion in July 1997 by Andrew Cunanan.
Versace and Blackstone both declined to comment to Reuters.
The reports of a sale come as Michael Kors has made it clear that it wants to transform itself into a house of luxury brands, starting past year with its acquisition of Jimmy Choo, made famous for its "Sex and the City" stilettos.
Rumours of an IPO have resurfaced since the company sold a 20 per cent stake to private equity giant Blackstone in 2014.
Michael Kors, whose namesake label is best known for its leather handbags, has made no secret of its ambition to grow its portfolio of high-end brands after buying British stiletto-heel maker Jimmy Choo for US$1.2 billion a year ago. The strategy follows moves by other fashion companies. Michael Kors couldn't immediately be reached. Kors is also trying to purchase Coach owner Tapestry Inc. Versace designs, manufactures and distributes clothes, jewellery, watches, eyewear, accessories and home furnishings that bear the company's distinctive Medusa logo.
In 2016, Versace poached Alexander McQueen's boss Jonathan Akeroyd to help it smarten up for a stock market listing, although that never materialised.
Versace does not disclose its financial details, but documents deposited with the Italian chamber of commerce show that past year it posted sales of 668 million euros (US$786 million) and earnings before interest, tax, depreciation and appreciation (EBITDA) of 44.6 million euros. Donatella serves as creative director, while Santo is chairman.
Those iconic $2,000-a-pop Gianni Versace gold-colored jackets once worn only by Hollywood elites, including Michael Jackson, Paul McCartney and Madonna, may soon become more affordable.