Toshiba added that it intends to reach a "mutually satisfactory" agreement with the consortium by June 28, the date of its annual ordinary general shareholders meeting. Toshiba also said it aims to close the deal by March 2018.
South Korean chipmaker SK Hynix and Japan's Mitsubishi UFJ Financial Group are in talks to provide financing for the deal.
Earlier this year, Toshiba shareholders gave the go-ahead for the sale of the memory business; Toshiba is the world's second largest producer of NAND flash memory — behind Samsung.
There have been several suitors for the memory business, including Taiwanese manufacturer Foxconn, SK Hynix and Broadcom.
Western Digital responded to the news, saying Toshiba ignored the rights of SanDisk — Western Digital's subsidiary — and the legal process currently under way. Western Digital jointly operates a semiconductor plant with Toshiba in Japan; the original joint venture agreement was signed with SanDisk before it was acquired by Western Digital.
In a prepared statement, Western Digital said: "Toshiba Corporation continues to ignore both SanDisk's consent rights and the dual-track legal process currently underway. The language of the relevant agreements is clear: Toshiba Corporation has no right to transfer its JV [joint venture] interests to a third party without SanDisk's consent. SanDisk has not given its consent to any transaction, and will continue to protect its JV interests and preserve its rights through both its request for injunctive relief and the arbitration process."
Last week, Western Digital said it sought an injunction to stop Toshiba from selling the business. A hearing is scheduled for July 14.
Analysts have previously said the sale of the memory business could be key to turn around the broader business, which booked a net loss of $4.86 billion in the nine months to December for the fiscal year that ended March 31, 2017.
After twice delaying the release of earnings, Toshiba finally announced the numbers in April, but it did so without auditor endorsement.
Toshiba shares closed down 2.18 percent at 323 yen.