Henkel & Co KGaA AG and Coty Inc, both of which have personal care and cosmetics businesses, made binding offers to buy separate parts of Procter & Gamble Co's beauty businesses worth up to a total of $12 billion, according to people familiar with the matter.

The bids, submitted on Monday, bring P&G one step closer to shedding several assets it considers non-core, as its chief executive officer, A.G. Lafley, presses on with his cost-cutting strategy.

Henkel made an offer for P&G's haircare business, which includes the Wella and Clairol brands, and could fetch a valuation of $5 billion to $7 billion, the people said. While Henkel is considered to be the most likely buyer, private equity firm KKR & Co LP also submitted a bid for the haircare business, the people added.

Coty, which makes perfume for fashion brands Calvin Klein and Marc Jacobs and owns nail polish brand OPI and Rimmel mascara, has submitted bids for P&G's fragrance unit and its cosmetics business.

Buyout firm Clayton Dubilier & Rice LLC also submitted a bid for P&G's cosmetics business, which includes drugstore brands CoverGirl and Max Factor and could fetch around $3 billion in a sale.

Warburg Pincus LLC, another private equity firm, is also interested in P&G's cosmetics business as well as its fragrance unit, which includes brands like Hugo Boss and Gucci and could fetch around $2 billion.

The sources asked not to be identified because the auction for the assets is confidential. Representatives for P&G, Coty, KKR, Clayton Dubilier & Rice and Warburg Pincus declined to comment while Henkel could not be reached for comment.

Lafley said last year he would reverse Cincinnati-based P&G's strategy of aggressive expansion and shed more than half its brands.

P&G has already divested some of its non-core brands. Last year, the company sold its Duracell battery brand to Warren Buffett's Berkshire Hathaway Inc for $4.7 billion and sold some of its soap brands to Unilever Plc.