Toshiba's used-memory chips are seen at an electronics shop in Tokyo November 9, 2010.
One of the companies rumored to be interested is Taiwan's Hon Hai, which bid more than $18 billion for the division according to Japan's Yomiuri Shimbun newspaper.
Toshiba officials were not immediately available for comment.
Nikkei reported that US private-equity firm Silver Lake Partners and American chipmaker Broadcom, part of the firm's portfolio, apparently tendered a roughly 2 trillion yen or $17.9 billion bid.
Toshiba had earlier not decided on the actual size of the stake sale, but is now reported to be ready to sell a majority stake or even its entire stake in the Nand memory chip unit, which makes memory chips for mobiles and tablets and is its most valuable business.
At the same time however it would have to deal with Toshiba's legacy clients, and either phase them out or enter the global memory business.
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Under the Congressional Review Act, the resolution only needed a simple majority to pass. In the Senate, Republicans have a 52-48 majority.
Three tech firms -Apple, Amazon, and Google -have reportedly joined the considerable list of bidders of Toshiba's NAND flash memory business, now on the market as Toshiba looks to raise $9 billion to cover losses at its USA nuclear unit, Westinghouse, AppleInsider reports.
Taiwan's Hon Hai, which acquired Japanese electronics- maker Sharp a year ago, has apparently bid more than two trillion yen (S$25 billion), the daily said. Toshiba plans on meeting with individual bidders this month.
Toshiba is the world's number two supplier of memory chips for smartphones and computers, behind South Korea's Samsung, and the business accounted for about a quarter of its 5.67 trillion yen in revenue last fiscal year.
The red ink is largely tied to huge cost overruns and construction delays at its USA nuclear power unit Westinghouse Electric, which filed for bankruptcy protection this week.
The American government has guaranteed loans of US$8.3 billion to help finance some of the construction of four reactors in the US.