NYK was spun out of the Mitsubishi Group long ago but has retained cross-holdings in a number of companies under the Mitsubishi umbrella.
The newspaper estimates NYK is looking to sell represents about one-sixth of the company's shareholding in various Japanese companies.
NYK, like other carriers, struggled in 2008 and 2009 and has engaged in numerous cost-cutting and cash-raising exercises in the last two years, including a sale of its own shares last year.