According to Reuters, A Toshiba spokesman said the company could not comment on details of the talks. A Western Digital representative declined to comment.
Toshiba has been trying to sell the unit for months to pay down debt and cover the impact of over $6 billion in liabilities linked to U.S. nuclear arm Westinghouse.
Toshiba wants to close the sale by the end of the fiscal year in March to ensure it does not report negative net worth, or liabilities exceeding assets, for a second year running. This could result in a delisting from the Tokyo Stock Exchange.
Given regulatory approvals could take six months, the company has been hoping to reach a deal by the end of August to ensure it can close the sale in time.
In addition to Western Digital, the consortium includes U.S. private equity firm KKR & Co and the state-backed Innovation Network of Japan and Development Bank of Japan. Sources have said the group was offering around 1.9 trillion yen ($17.5 billion) for the business.