An announcement is not expected to be made on Tuesday – the same day US voters go to the polls – but could be made soon, the Financial Times reported, citing unnamed sources.
Apax is understood to have partnered with former Converse chief executive Jack Boys, who is expected to take the helm at Cole Haan following the buyout, the report said.
TPG Capital and Berkshire Partners are also said to have been interested in the business.
The sale of the unit will help free up cash for Nike, which in May pledged to sell Cole Haan and football kit maker Umbro in a bid to refocus on its core business.
Nike, which bought Cole Haan in 1988 for $80m, has hired Goldman Sachs to handle the sale.
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