LONDON — Michael Kors is close to announcing a deal to buy Versace, the Italian fashion house, in its latest step toward becoming a rival for Europe’s luxury conglomerates, two people with knowledge of the matter said Monday.

The sale would mark the end of independence for one of the most prominent stand-alone fashion houses amid a wave of consolidation within the industry.

Last month, Ermenegildo Zegna acquired an 85 percent stake in Thom Browne, in a deal that valued the American fashion company at $500 million. In June, the Spanish luxury group Puig acquired a majority stake in Dries Van Noten, one of Europe’s last outstanding independent labels, for an undisclosed price.

And in May, Richemont, which owns brands including Cartier and Montblanc, acquired the luxury e-commerce group Net-a-Porter after an offer of 2.8 billion euros, or about $3.3 billion.

