Dow Chemical and DuPont, two of the biggest and oldest companies in the American chemical industry, are in talks to merge in what would be one of the largest transactions in a year full of huge deals, people briefed on the matter said on Tuesday.

Under the terms being discussed, a merger of the two companies — each with a market value of roughly $60 billion — could eventually be followed by a breakup of the company, two of these people said.

Combined, the two companies would be the second-biggest chemical company in the world, in terms of revenue, after BASF of Germany, with more than $92 billion in annual sales. The next step being discussed would be to break up the merged company into three businesses: agricultural chemicals, specialty products, and materials, like plastics.

An announcement could come soon, these people added, while cautioning that talks were incomplete and could still collapse.