The newspaper said Toshiba will announce the agreement on Wednesday and sign after a board meeting on September 20.
A new Reuters report has claimed that the two companies are in ongoing talk over the acquisition, which could be worth as much as $18.3 billion.
Toshiba did not immediately respond to requests for comment.
Yoshimitsu Kobayashi, an external Toshiba director, said at a press conference on Tuesday at the Keizai Doyukai group of corporate executives, that though the deadline is important, it is also important that negotiations head in a good direction.
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A Western Digital spokeswoman also declined to comment.
Through a consortium deal reported by Reuters, Western Digital and the Innovation Network of Japan could offer up to $17.4 billion to purchase the entirety of Toshiba's chip business. The offer by the consortium, which is led by the US private equity group and South Korean chipmaker SK Hynix as well as Japanese state-backed investors, was higher than an initial offer of around $18 billion, according to Reuters. The sale iinvolves 18 Billion and is sold to a consortium in which Western Digital (who previous year acquired Sandisk as well) has a large stake. -South Korean group had said that Bain Capital and other entities in the group would take over INCJ and DBJ's investment until the legal spat with Western Digital is resolved while raising the price tag for Toshiba Memory Corp to 2.4 trillion yen, becoming a strong contender. But those talks lapsed as Japan government investors who had been part of that consortium told Toshiba they were reluctant to close a deal in the face of the legal challenges posed by California-based Western Digital, which jointly invests in Toshiba's key NAND memory plant in central Japan.
Some media are also reporting that Bain Capital-backed consortium has upped its offer in the matter to $22.3 billion.
All three bidder groups have roped in major chip buyer Apple Inc (AAPL.O) to bolster their offers, sources have said.