The end game is fast approaching at Procter & Gamble Co. and its beauty operations.

Bids in the second and final round of a Goldman Sachs-run auction for a large part of the consumer product giant’s beauty business came in on Monday. Hair-care, cosmetics and fragrances brands are all on the block and could be sold in deals valuing the combined businesses at more than $10 billion, sources said.

Henkel AG & Co. and Coty Inc. were among the strategic acquirers vying for pieces of the portfolio, while the private equity companies in the mix included KKR & Co., Warburg Pincus and Clayton Dubilier & Rice, according to sources.

Henkel and KKR each made an offer for the hair-care business, which includes Wella and Clairol and is said to be valued at between $4 billion and $6 billion.

Coty turned in bids for the company’s fragrance business, which could fetch $2 billion, and the cosmetics business, valued at around $3 billion.

Warburg is also said to be looking at the cosmetics and fragrance units, while Clayton Dubilier & Rice is in the running for the cosmetics operations, which includes Cover Girl and Max Factor.

Also, bankers said Revlon has been eying P&G’s color and skin-care businesses, although it was unclear whether the company submitted a bid in the auction.

Representatives from Goldman and the bidders either declined comment or could not be immediately reached.

But investors in the U.S. generally appeared to be keen on the prospects of a deal. On Wall Street, P&G stock closed up 1.5 percent to $78.90, while Coty shares rose 0.9 percent to $25.74. Henkel shares ended down 0.3 percent to 89.15 euros, or $99.50, in Frankfurt.

William Susman, managing director at advisory and research firm Threadstone Partners, said the brands for sale were “most conducive for a strategic acquirer given their size, the importance of realizing synergies and the need to have management to run the businesses.”

Susman noted that brands such as Cover Girl, Max Factor and even Wella are still connecting with shoppers, but “at a declining pace.”

“Like any brand, they require continued investment, marketing and product development,” he said. “Without it, these brands will continue to decline.”

While the P&G properties are attractive to strategics that might not want to take the chance of buying an indie brand, private equity companies could be looking for a way into the sector.

One banker said Warburg Pincus is bidding with an eye toward setting up a platform that could be used to make other acquisitions. Instead of trying to cobble together several small beauty brands and then building an infrastructure, the banker said, “It’s easier to buy a group in a certain space, keep the management and distribution and then do add-ons to build out the platform.”

However it turns out, the auction, some details of which were first reported by Reuters, could help reset the balance of power in the beauty sector. As P&G takes a step back, others in the industry will be given more room to expand.

Olivia Tong, research analyst at Bank of America Merrill Lynch, said Coty’s bid presents an “interesting opportunity” for the company from a brand perspective. And from a strategic view, she said the move also makes sense since Coty “has, historically, been a growth by acquisition company.”

P&G is staying in the beauty business, but to a lesser extent. At the WWD Beauty Summit in New York, Alex Keith, president of the group’s global skin and personal care, said, “Is P&G getting out of beauty? The answer is a resounding ‘no.’” She said she returned to beauty seven months ago to “get our beauty business back on track.”

The auction marks a key milestone for chairman and chief executive officer A.G. Lafley, who not only built up P&G’s beauty business during his first stint as ceo, but last August started the streamlining process that sees the company now spinning off scores of brands. By the time it’s done, Lafley’s plan to boost profits by making the company leaner and meaner will have cut 80 to 90 of the company’s 160 brands.

P&G already sold the Rochas fragrance and fashion business to Inter Parfums for $108 million in March. Last month, the Frédéric Fekkai business was acquired for $50 million by Fekkai Brands, a joint venture between Designer Parfums and Luxe Brands.

The sweeping changes at P&G have had tongues wagging about exactly what might happen at the company.

“P&G was culturally unprepared to succeed in cosmetics,” one insider told WWD’s sister publication Beauty Inc. recently. “Their big play was to make the beauty business look like their other successful businesses, but the drivers of beauty are different. They never understood the emotional benefits, the purely female benefits, of beauty.

“They were used to winning with product innovation and huge volume categories,” the insider said. “They weren’t used to image management and winning in a desire-based business. They never got the emotional benefit of making a woman feel beautiful.”

One oft-heard opinion is that P&G regularly used innovation, rather than emotion, as a marketing message.

One example is Cover Girl’s LashExact mascara, which featured a first-to-market technology with a molded silicone brush. Historically, mascara is a category dominated by L’Oréal, which controls many design patents for bristle-brush wand technology. In 2006, Cover Girl spent an estimated $1 million on silicone brush molds to gain market share in the category in a major way. The plan worked — kind of. Cover Girl’s mascara business skyrocketed.

Eventually, though, competing brands acquired the technology—and in the meantime, Cover Girl’s marketers had taken their eyes off the bigger business. “They took the lead in mascara away from Maybelline,” said one analyst, “but they spent so much time doing it that they lost their dominance in the face business, which was their traditional power base and has the highest loyalty factor in cosmetics.”

The divestitures will give P&G an opportunity to focus more on its remaining, larger businesses, while new players get a chance to put their mark on established brands across the beauty landscape.