Blackstone would sell its 20 percent stake as part of the deal, according to the Wall Street Journal.
The deal is expected to close in the fourth fiscal quarter, subject to regulatory approvals.
The deal comes as budding luxury conglomerates, including Michael Kors' U.S. rival Tapestry, owner of Coach and Kate Spade, are trying to make inroads into an industry still dominated by major European players, including Louis Vuitton owner LVMH.
It is learnt that the USA fashion group has agreed to buy the Italian firm in a deal worth about €1.7bn ($2bn, £1.5bn), This is coming just a year after Michael Kors bought Jimmy Choo, the luxury shoemaker founded in London, for nearly £900m.
"Why just WHY would you sell Versace to a brand like MICHAEL KORS", says another. There have even been guessing games as to what Michael Kors would rename his holding company, should he choose to do so. The strategy follows moves by other fashion companies.
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Gianni Versace founded his company in 1978 in Milan, building it into an worldwide powerhouse by the time that he was shot at the age of 50 by Andrew Cunanan, a serial killer who murdered at least four other people, in 1997.
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.
Michael Kors also announced previous year it would go fur-free, which makes the Versace acquisition all the more in line with its values.
Blackstone, whose stake acquisition valued Versace at $1.4 billion in 2014, declined to comment. However, Versace has struggled to grow sales, despite a luxury-fashion boom led by Chinese consumers. Donatella Versace is now the chief designer of Versace Group, and sister of its founder. She is artistic director of the fashion house.
Models present creations at the Versace show during Milan Fashion Week Spring 2019 in Milan, Italy, September 21, 2018. In a tribute to Gianni, Donatella Versace brought back the most iconic looks from his collections spanning the 1990s, including silk blouses mixing leopard prints with images of baroque architecture.