KKR & Co LP and Carlyle Group LP are competing for National Vision Inc, the fourth-largest U.S. retailer of eyeglasses and contact lenses, in an auction that could fetch up to $1 billion, people familiar with the matter said this week.

The two private equity firms are among those making it past the first round of an auction for National Vision, the people said. Meetings with the company's management are currently under way, before solicitation of final offers, they added.

The Lawrenceville, Georgia-based company, which is owned by private equity firm Berkshire Partners LLC, is working with Barclays Plc on the sale process, people familiar with the matter have previously told Reuters. 

Berkshire Partners, KKR and Carlyle declined to comment, while National Vision did not respond to a request for comment.National Vision, which focuses on low-cost glasses and contacts, operates more than 700 retail locations in 43 states under chains that include America's Best Contacts & Eyeglasses and Eyeglass World. It competes in the United States with Luxottica Group Spa, Wal-Mart Stores Inc and Visionworks of America Inc.

Last year National Vision extended for five years a partnership with Wal-Mart that allows it to manage 227 stores within Wal-Mart, according to Standard & Poor's Rating Services Inc.

National Vision also has stores inside retailer Fred Meyer Inc KR.N and military bases, and sells its products online. The company employs more than 6,000 people, according to its website.

Berkshire Partners took National Vision private in 2005 in a $190 million deal that was funded with $153 million in debt and included the simultaneous acquisition, for $88 million, of Consolidated Vision Group Inc, an optical chain that was backed by private equity firm Kelso & Co.The buyout firm has more than recouped its original 2005 investment in the company, even before any sale.

This is because National Vision last year carried out a dividend recapitalization, borrowing $300 million to fund a $117 million dividend, according to Moody's Investors Service Inc. That followed an $88 million dividend two years earlier funded through more debt, according to Thomson Reuters Loan Pricing Corp.

Boston-based Berkshire Partners, which raised its latest $4.5 billion fund in 2011, has invested in several other retail companies, including women's apparel chain Aritzia and jeans maker Citizens of Humanity.