Eastern Airlines and Braniff International are holding discussions about a possible merger, the two companies announced yesterday.

Officials of both airlines declined to elaborate on the status of the talks, the way in which the companies might merger or any timetable. "All we're doing is going to take a look at the two companies to see if it makes any sense to go ahead," Jim Ashlock, spokesman for Miami-based Eastern, said yesterday. "If it looks like the merger makes sense, then we'll make a formal application."

Jere Cox, spokesman for Dallas-based Braniff, also declined to elaborate, stressing only that the discussions were in the "very beginning of the preliminary stage."

A merger would require the approval of the boards of both companies, their stockholders, the Civil Aeronautics Board and the White House because international routes would be involved. A proposed merger probably also would have to be cleared by the two airlines' creditors.

Neither carrier has been at the top of any stock analyst's "buy" list recently. But Eastern, considered near bankruptcy five years ago, is now the stronger of the two, and Braniff, a consistently profitable carrier until last year, is considered to have serious financial troubles now. It is assumed in the industry and on Wall Street that Eastern would acquire Braniff if an arrangement is worked out.

"I think it would be a good thing . . . probably for both, although better for Braniff," Michael Derchin, an analyst with Oppenheimer & Co., said yesterday. "Braniff was up today and Eastern wasn't, so it looks like the market agrees with that," he added. In New York Stock Exchange trading yesterday, Braniff closed at 5, up 1, while Eastern was unchanged at 7.

A merger would provide Braniff with a link to a carrier considered stronger and able to help the Dallas-based airline get through some of its current difficulties, Derchin said. A merger would given Eastern access to Braniff's lucrative Latin American routes, which are limited by strict bilateral agreements, and to a young fleet of modern planes, he noted.

The problems the carriers might encounter from a proposed merger are the same ones that have plagued the Pan American World Airways merger with National Airlines and the merger of North Central and Southern into Republic -- combining different labor forces and aircraft into a cohesive system, industry observers said yesterday.

Braniff suffered a record loss of $44 million in 1979 and has chalked up a net loss of $51.6 million for the first nine month of this year. It did report earnings of $18 million in the third quarter, due at least in part to the sale of some of its aircraft. Many industry observers believe Braniff's problems stem in large part from a very ambitious program to expand its route system once airline deregulation was enacted. Immediately following the expansion, jet fuel prices doubled and passenger traffic fell off as the economy turned sour. Braniff recently has been cutting back the routes it had added and its work force.