Dow Chemical Co. is in late-stage talks to merge with DuPont Co. in what would be the largest deal in the chemicals industry, people with knowledge of the matter said.

An accord may be announced as soon as this week, said the people, who asked not to be identified because the information is private.

After the merger, the company would break into two or three businesses because of regulatory and other issues, the people said. There’s no guarantee a deal will get done, and talks may still fall apart, the people said.

The transaction would combine two of the most storied names in U.S. industry and create the world’s second-biggest chemical company behind BASF, as well as the largest seed and pesticide company, surpassing Monsanto. Representatives of both companies declined to comment. The Wall Street Journal reported the merger talks earlier.

This year has already been a tumultuous one for DuPont, whose former chief executive, Ellen Kullman, stepped down in October, about five months after winning a proxy battle waged by an activist investor. Dow CEO Andrew Liveris led the company’s recovery from near-insolvency during the financial crisis and has faced pressure from an activist shareholder: Dan Loeb’s Third Point.

DuPont and Dow, which have stock market capitalizations of $58.4 billion and $59 billion respectively, have in recent months confirmed they were weighing options for their agricultural chemicals businesses, both of which supply genetically modified seeds. There’s been widespread speculation about potential deals in that industry as lower crop prices curb farmer spending, and after Monsanto’s bid for Syngenta, which was withdrawn in August. It’s a “game of musical chairs going on between the ag-chem companies,” analyst Hassan Ahmed, of Alembic Global Advisers, said Wednesday in a Bloomberg Television interview.

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The split following a Dow-DuPont merger would probably involve creating a company focused on agricultural products such as crop seeds and pesticides, another focused on specialty chemicals and a third that makes plastics and other commodities, according to Manhattan-based Ahmed. Total cost savings may be $3 billion to $4 billion, he said.