The deal values the fashion house, known for its Medusa head logo, at no less than $2 billion, two of the sources added.
It was learned that Michael Kors organization would do the acquisition themselves.
The Versace family owns the rest of the company.
The deal gives Michael Kors a mega-brand and red carpet favourite that is among the most recognizable and followed fashion labels in the world.
Versace declined to comment.
Versace has been considering a listing, after U.S. private equity group Blackstone bought a 20% stake in 2014 to fund overseas expansion, although Chief Executive Jonathan Akeroyd told Reuters earlier this year there was no rush for a market debut.
Last year, Michael Kors bought Jimmy Choo, the luxury shoemaker founded in London, for nearly £900m.
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.
An official announcement is expected this week, the sources said. Silas Chou and Lawrence Stroll, former investors in the Kors business, are not involved in this deal, sources said. A spokesman for Blackstone had no comment.
In recent years, Versace, which is still a favor among celebrities, has struggled to grow sales and has become second to its Italian rival Gucci, who has found a way to grow, especially among millennials.
The brand has been at its most prominent in years since a hit show last September at Milan Fashion Week.
Versace founded his namesake company in 1978 in Milan, growing it into an global powerhouse by the time he was gunned down by a serial killer in 1997. Donatella serves as creative director, while Santo is chairman.
Versace had revenue of €686 million euros and returned to profit in 2017, according to figures provided by the company.