Western Digital Corp. plans to present Toshiba Corp. with a revised offer for its memory chip unit next week in order to resolve an increasingly bitter conflict over the future of a business the two companies jointly own, according to a person familiar with the matter.

The U.S. company’s Chief Executive Officer Steve Milligan will travel to Tokyo next week to meet Toshiba President Satoshi Tsunakawa, the person said, asking not to be identified because the details are private. The new plan is designed to make it more palatable for Toshiba shareholders to accept an acquisition by Western Digital and its associates, according to the person, who wouldn’t specify the price to be offered or name partners.

The two companies have been increasingly at odds over Toshiba’s plan sell its flash memory business in which Western Digital is a manufacturing partner. While Toshiba needs to raise cash to keep itself afloat following a disastrous investment in nuclear power, Western Digital has sought to block the sale on concerns the operations may fall into the hands of competitors. The U.S. company has not been able to match other bidders and has instead sought legal remedies to delay the sale.

Toshiba climbed as much as 3.3 percent in Tokyo, while Western Digital’s stock rose 1.7 percent in U.S. trading.

Deal of the Week: Toshiba Memory Chip Sale Hinges on Nationalism

As of a May 19 deadline for second-round offers, Broadcom Ltd. and a group led by KKR & Co. had emerged as the two leading bidders for the chip unit, people familiar with the matter said at the time. Broadcom, based in San Jose, California, is offering about 2.2 trillion yen ($20 billion) and would face simpler regulatory reviews than some rivals, said one of the people.

The group led by KKR plans to offer about 1.8 trillion yen and may receive support from the country’s government, the people said. KKR’s group may include Innovation Network Corp. of Japan and Development Bank of Japan, both state-sponsored investment vehicles. Western Digital had been in discussions to join the group, but it was offered a stake of less than 20 percent.

Western Digital’s revised plan will not call for a controlling stake and will leave room for participation of partners, including INCJ and DBJ, the person said on Thursday. The U.S. company will eventually seek control of the venture, according to the person. Western Digital offered about 1.5 trillion yen in the first round of bidding, a separate person familiar with the details said.

Toshiba sent a letter to Western Digital’s chief legal officer on Wednesday saying it’s moving assets from the joint venture back to the parent company after transferring them to a subsidiary in preparation for the sale. The U.S. company had previously said the change triggered an arbitration clause in their business agreement, which could delay a sale Toshiba needs to complete quickly.

Returning the assets makes the claims moot, Toshiba said in the letter from its lawyer at Morrison & Foerster. Western Digital responded in a statement, saying it has no plan to withdraw its arbitration claim and sees no reason to believe the breach of agreements is resolved. Any attempts at a sale of the unit violate Western Digital’s rights, the company said.

The other bidders for Toshiba’s chips business are Taiwan’s Hon Hai Precision Industry Co. and South Korea’s SK Hynix Inc. They face long odds because of political and antitrust opposition.