PARIS (Reuters) — Henkel AG & Co. KGaA  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 hair-care 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 hair-care 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.