Western Digital Corp. is in advanced talks to merge with Japan’s Kioxia Holdings Corp., according to people familiar with the matter, in a deal that could be valued at more than $20 billion and further reorder the global chip industry.

Long-running discussions between the companies have heated up in the past few weeks and they could reach agreement on a deal as early as mid-September, the people said. Western Digital would pay for the deal with stock and the combined company would likely be run by its Chief Executive, David Goeckeler, the people said.

There’s no guarantee Western Digital, which had a market value of around $19 billion Wednesday afternoon, will seal an agreement, and Kioxia could still opt for an initial public offering it had been planning or another combination.

The Wall Street Journal reported in March that Western Digital and Micron Technology Inc. were examining potential deals with Kioxia, which makes NAND flash-memory chips used in smartphones, computer servers and other devices. Micron’s interest has since cooled and Kioxia has been focused on discussions with Western Digital, which already has deep existing ties with the Japanese company.

Any transaction would require the blessing of the Japanese government, given Kioxia’s significance there and the political sensitivities of transferring ownership of such key technology. Washington would also likely play a role, but a deal could fit with a push by the U.S. to boost its chipmaking capabilities and increase competitiveness with China.

Perhaps the biggest regulatory hurdle would be China, which has been increasingly aggressive in its antitrust enforcement, helping scuttle potential deals including Qualcomm Inc.’s proposed $44 billion purchase of Dutch chip maker NXP Semiconductors NV in 2018.

There has been a burst of acquisition activity among chip makers, with the industry accounting for several of the biggest deals of the past few years. Those include Advanced Micro Devices Inc.’s roughly $35 billion purchase of Xilinx Inc., Nvidia Corp.’s roughly $40 billion buyout of SoftBank Group Corp. -backed Arm Holdings and Analog Devices Inc.’s $20 billion acquisition of Maxim Integrated Products Inc.

In a sign of how difficult it can be to get such deals across the finish line, Nvidia last week said getting approval for its proposed purchase of Arm has progressed only slowly. U.K. regulators are assessing whether to give their blessing to a deal that also still needs approval from other governments. China only just recently approved Analog’s purchase of Maxim, more than a year after the deal was first struck.

Intel Corp. meanwhile, has made clear it is interested in acquisitions and has explored purchasing GlobalFoundries Inc. The chip-production firm, owned by an investment arm of the Abu Dhabi government, is planning an IPO and has so far been unreceptive, however.

(Intel last year agreed to sell most of its memory-chip business to South Korea’s SK Hynix Inc. )

Demand for memory chips has been hot, lifted by new smartphone launches, 5G expansion and demand for PCs and servers. Samsung Electronics Co. , the world’s largest memory-chip maker, last month said roaring demand helped offset weakness in smartphone shipments. In a reflection of the demand, flash-memory prices have shot up in recent months.

That has helped Kioxia’s valuation since it backed away from a planned IPO last fall, citing the coronavirus pandemic and market volatility. It was expecting a valuation then of around $16 billion.

Western Digital, which makes hard disk drives, solid-state drives and NAND chips, has a joint venture with Kioxia for manufacturing and research and development that was set to expire starting in 2027. That agreement appears to have given Western Digital a leg up on Micron, which has a market value of $83 billion and could have more easily pulled off a full takeover.

Their existing ties could help make a WD-Kioxia combination more palatable to regulators.

Western Digital shares rallied on the news that it was exploring a deal with Kioxia, closing up 7.8% Wednesday at $65.50 after the Journal’s report on the talks. That could indicate shareholders are supportive despite what a large bite it would be.

Kioxia, formerly part of Toshiba Corp. and known as Toshiba Memory, was purchased in 2018 by a group led by private-equity firm Bain Capital that included Apple Inc., Dell Technologies Inc., Kingston Technology Co. and Seagate Technology PLC, for around $18 billion. Toshiba retained a 40% stake in the business, which was renamed Kioxia the following year.

Write to Cara Lombardo at cara.lombardo@wsj.com and Dana Cimilluca at dana.cimilluca@wsj.com