LONDON — Bayer AG is proposing an increased offer and break fee as it tries to clinch the acquisition of Monsanto Co. to create the world’s biggest maker of seeds and pesticides, according to people familiar with the matter.

Bayer is willing to raise its offer to about $129 a share, or $56.5 billion, from $127.50 a share, and double the antitrust break fee to about $3 billion, said the people, who asked not to be identified because the deliberations were private.

Monsanto’s management board was scheduled to discuss and potentially approve the proposal, the people said. Bayer’s supervisory board is set to review the deal Wednesday, and an announcement could come shortly thereafter, the people said. Talks may still fall apart.

The bid is 22 percent above Monsanto’s closing price on Tuesday in New York. If successful, it would lead to the biggest deal this year and the largest ever by a German company. Monsanto shares fell 89 cents to close at $106.10 in New York. Bayer declined 0.3 percent to close at 93.30 euros in Frankfurt, valuing the company at 77.2 billion euros ($86.6 billion).

Bayer’s wooing of Monsanto has played out against a backdrop of a rapidly consolidating crop and seed industry as falling crop prices cut into profits.

A series of big deals may leave just a few global players. China National Chemical Corp. agreed in February to acquire Syngenta AG, while DuPont Co. and Dow Chemical Co. plan to merge and then carve out a new crop-science unit.