Shares of Coty Inc. shot up 17.4 percent in early trading today on reports that the beauty company was close to a $12 billion deal to buy CoverGirl, Max Factor, Wella and other hair care businesses from Procter & Gamble Co.

If the deal, which was first reported by the New York Post, were to close, it would make the fragrance-heavy Coty a much bigger player in the beauty space. But the reported deal would be a huge one for Coty to swallow – even with Tuesday morning’s stock boost, which sent the firm’s shares up $4.54 to $30.59, the company has a market capitalization of just over $11 billion.

Goldman Sachs, which is running the auction, took final bids last week with Henkel AG & Co. and private equity firms KKR & Co., Warburg Pincus and Clayton Dubilier & Rice all submitting bids, according to sources. P&G chairman and chief executive officer A.G. Lafley is selling off the beauty businesses so the consumer products giant can focus on fewer brands.

While the P&G businesses would be a big deal for Coty, the company has shown a big appetite in the past, making an unsuccessful run at buying Avon Products Inc. for $10 billion or more in 2012.