The chief executives of Toshiba and U.S. chipmaking partner Western Digital agreed Wednesday to discuss the Japanese conglomerate's sale of a majority stake in its flash memory unit, which Western Digital has opposed selling to any buyer but itself.

Toshiba President Satoshi Tsunakawa and Western Digital CEO Steve Milligan met in Tokyo Wednesday afternoon.

Both sides appear to have moved to end the standoff over the sale in the interest of preserving their joint production arrangement in Japan.

Western Digital has offered to buy Toshiba Memory, which was recently spun off from the Japanese parent, but its initial bid is lower than others at this point. Toshiba has sought at least 2 trillion yen ($17.8 billion) from the sale.

Last week, Western Digital said it formally requested an arbitration with Toshiba through the International Chamber of Commerce which could complicate or delay Toshiba's plan to sell the unit. The U.S. company maintains that Toshiba doesn't have the right to sell its stake in the joint venture between the two companies to a third party without Western Digital's consent and wants exclusive negotiating rights to the buy the business.

However, Western Digital seems to have already increased its offer for Toshiba's semiconductor business, offering nearly $17.8 billion, according to a report Wednesday by the Japan Times.

Such a bid would represent a sizeable increase from the roughly $14 billion Western Digital reportedly offered previously and would be in the ballpark of what other suitors, including Broadcom, SK Hynix and the combination of private equity firm Kohlberg Kravis Roberts (KKR) with Innovation Network Corp. of Japan (INCJ) are thought to have offered.

Hon Hai Precision Co. reportedly offered as much as $27 billion to acquire Toshiba's chip unit.