Aetna is near an agreement to buy its smaller rival Humana for about $34 billion, people briefed on the matter said on Thursday, in what could be the first in a series of mergers among the country’s big health insurers.

Under the terms, Aetna would pay roughly $230 a share in cash and stock, the people said. That is almost 29 percent higher than where Humana’s shares were trading before the emergence of news reports that the company was considering selling itself.

A deal between Aetna and Humana could be imminent, though people briefed on the talks said that a formal agreement had yet to be signed and that the discussions could still fall apart.

Many of the country’s big health insurers have been rushing toward a new round of consolidation, seeking to gain greater scale and wring out costs from their operations. Such belt-tightening is increasingly important because many of the new customers that insurers are seeking are more sensitive to the price of health coverage.