Givi in turn is half-owned by Allegra Versace Beck, daughter of Donatella and niece of late founder Gianni.
Versace had revenue of 686 million euros and returned to profit in 2017, according to figures provided by the company.
Blackstone Group LP owns 20 percent of Versace, which sells leopard-print sweatshirts for 2,100 euros ($2,470) and 995-euro tartan-covered sneakers. Bloomberg and Reuters news agencies later reported the buyer would be fashion group Michael Kors.
Michael Kors and Tiffany could not immediately be reached for comment.
Neither Versace or Michael Kors are yet to release a statement regarding the sale at this present time.More news: Julie Chen leaving 'The Talk' following husband Les Moonves' CBS exit
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Headquartered in London, Michael Kors who has its roots are in the United States, could announce a deal as soon as this week, said the reports which cited unnamed sources.
The stark difference between Michael Kors and Versace has some fans revolting against the rumoured deal on social media.
It is unclear whether the Versace family, which has controlled the brand for decades, would remain as minority shareholders in the business or if Donatella Versace would stay on as creative director. A spokesman for Blackstone had no immediate comment.
For more on reports of Michael Kors purchasing Versace, follow on over to Reuters.
Versace had planned to float the company on the stock market but put the plans on hold owing to unfavourable conditions.
"A continued prominent role for Donatella Versace will be vital in short-term, until a suitably high-profile or high potential candidate can be found to take the fashion house forward, in a similar way to how Christopher Bailey steered Burberry and Alessandro Michele has reinvigorated Gucci", he added. The 40-year-old fashion house returned to profit in 2017 and reported revenue of almost $800 million.