Coty Inc. has kicked off the sale of its professional hair and nail products business, drawing interest from some of the world’s largest buyout firms for a unit that could fetch as much as $8 billion, according to people with knowledge of the matter. Buyout firms including Advent International, Bain Capital and Cinven are working with advisers to prepare bids, the people said, asking not to be identified because the discussions are private. Clayton Dubilier & Rice LLC and KKR & Co. are also expected to make first-round bids, which are due the first week of March, the people said. Henkel AG, a German maker of adhesives and shampoos, has hired advisers as it explores a bid for the business, which could fetch $7 billion to $8 billion, the people said. Other strategic bidders including Unilever Plc are weighing offers for parts of the unit, the people said. No final decisions have been made and the talks about a sale remain in the early stages, the people said.