A truce, which might also include potential changes to Western Digital’s board, could be unveiled as soon as this week, assuming the talks don’t fall apart, the people said.

San Jose, Calif.-based Western Digital, which has a market value of around $19 billion, previously said it would consider Elliott’s ideas. At a conference in late May, Western Digital Chief Executive

David Goeckeler

said the company and Elliott have been discussing additional ways to improve the company’s valuation.

“Their letter was very constructive,” he said. Western Digital in 2020 decided to form separate units for its two businesses, a move Elliott praised and some saw as a precursor to a potential split.

Meanwhile, Japanese chip maker Kioxia Holdings Corp. is still open to a possible deal with Western Digital, some of the people said.

Western Digital and Kioxia previously had been speaking since early 2021 and were working on a stock deal that would have created a memory-chip powerhouse, The Wall Street Journal reported last summer. But the talks stalled months later, partly because of a steady decline in Western Digital’s shares.

Kioxia’s business would be a logical fit for Western Digital’s flash unit, which Elliott estimated could command an enterprise value of $17 billion to $20 billion, roughly equal to Western Digital’s market capitalization before its shares rose when Elliott’s campaign surfaced.

Elliott also said in the letter to the company that it would invest an additional $1 billion or more in equity in a potential spinoff or merger of the flash business in conjunction with another industry player.

Write to Cara Lombardo at cara.lombardo@wsj.com