Reuters previously reported that parent company Hitachi Ltd has been planning to sell its 53% stake in the unit, which makes components for cars and industrial equipment, as it streamlines its operations.
Hitachi said on Friday "no formal decision has been made" with regards to the reported sale of Hitachi Metals, adding that the firm was considering "the enhancement of its corporate value".
Initial bidding will be closed by the end of this month, said one of the sources, all of whom spoke on condition of anonymity as the bidding is not public.
Representatives for Carlyle, Bain Capital and KKR all declined to comment. Representatives for Apollo Global Management were not available for comment.
Hitachi Metals shares rose almost 10% on Friday, after the Nikkei business daily initially reported KKR and Bain Capital were among the bidders.
The deal would be the latest by private equity in Japan this year. This week KKR agreed to buy a majority stake in Japanese supermarket chain Seiyu with an e-commerce company Rakuten for over $1 billion.
Minority shareholders in the Hitachi unit are expected to sell their stakes to a winning bidder and the company would eventually be delisted, according to the previous Reuters report.
Hitachi Metals has a market value of about 660 billion yen ($6.4 billion) based on Friday's close. A buyout would likely exceed that, given that a premium would be expected.
Reuters also previously reported Hitachi had retained Goldman Sachs Group to advise on the sale, while Hitachi Metals has hired Bank of America.
($1 = 103.8000 yen)
(Reporting by Junko Fujita, additional reporting by Makiko Yamazaki; Editing by Ana Nicolaci da Costa)
By Junko Fujita