John Connaughton, Bain's co-managing partner, confirmed the firm is working with Apple and Dell Inc., without disclosing details of the negotiations.
Thursday's drop came as Toshiba's U.S. chip factory partner, Western Digital, vowed to keep trying to block the sale in court.
To this, Toshiba responded by claiming that Westerbn Digital "persistently overstates its limited consent rights in public statements".
Toshiba has been working toward the deal since January, when the struggling company announced it would be looking for bidders to acquire its lucrative chip business in an effort to raise some much-needed capital. Things, however, fell through a day before Toshiba made the final decision.
Western Digital Corporation has sought to prevent the sale of the interests of the Joint Ventures to any third party, and the two parties are now engaged in litigation and arbitration.
Enclosed in Wednesday's agreement, Bain Capital has agreed to complete the deal regardless of legal challenges.
Apple is interested in the chip unit because of the strategic importance of flash memory. This group includes SK Hynix from South Korea, Bain Capital from the US, and INCJ (Innovation Network Corporation of Japan), which is a Japanese public and private fund, and political investment banks from Japan.
Fellow storage giant Western Digital had been thought to be in pole position to snap up Toshiba's operation, with shares in the company falling following the Bain Capital news.
Because of the presence of Hynix, a competitor to Toshiba in the NAND flash business, a sale to the Bain group will be subject to anti-trust scrutiny.
In addition to the joint investment at Yokkaichi, Toshiba works with Western Digital on chip development.
On the heels of Toshiba's announcement, Western Digital announced that several of its SanDisk subsidiaries have filed an additional request for arbitration with the ICC International Court of Arbitration related to three NAND flash-memory joint ventures operated with Toshiba.
However, there is concern among experts who say that they have to pay attention to how many actual profits SK Hynix will make through the deal as SK Hynix does not take over equities with the management right.
Bain then revised its offer too.