Nike Inc. is nearing an agreement to sell its Cole Haan brand, according to multiple reports pegging private equity firm Apax Partners as the winning bidder.

Should the sale be announced in the next week as expected, it would conclude an auction process that began six months ago when Nike revealed plans to streamline its product offerings. Among the units being shopped to buyers were Umbro, a maker of soccer-related products that was sold to Iconix Brand Group Inc. (Nasdaq: ICON) for $225 million in October, and Cole Haan, a maker of footwear, clothing and leather handbags.

London and New York-based Apax reportedly outbid several rival private equity firms, including TPG Capital Management, Sycamore Partners and Berkshire Partners. The price tag is expected to be around $500 million.

While Nike would receive a return on Cole Haan, which it first acquired in 1988 for $80 million, it took a loss on Umbro, which was purchased in 2008 for $565 million.

Beaverton, Ore.-based Nike also didn't fair so well on the M&A landscape in 2008, when it sold Canstar Sports Inc., known for its hockey brand Bauer, to private equity firm Kohlberg & Co. for just $200 million, almost 50 percent less than what it paid for the business in 1995.

Cole Haan currently has more than 80 of its own retail stores, and is based in Scarborough, Me. and New York.