PITTSBURGH (AP) _ A boom in the number of heart transplant centers has crippled the already swollen transplant system, and the government has drafted guidelines to curb the trend and weed out borderline programs.

''It's the most significant problem in organ transplantation today,'' Dr. Robert J. Corry, president of the American Society of Transplant Surgeons, said recently. ''There are hospitals doing this that aren't qualified.''

The Health Care Financing Administration guidelines are expected to become official any day with their publication in the Federal Register, according to Ron Milhorn, a policy analyst with the agency.

Heart transplant centers would have to meet the guidelines to qualify for Medicare reimbursements. ''What they're designed to do is measure a facility's commitment to a heart transplant program,'' said Milhorn.

There are 93 heart transplant centers in the United States today, nearly triple the number three years ago, according to the U.S. Department of Health and Human Services.

Longtime leaders in the field contend that the proliferation is diluting the already depleted pool of donor organs. That, plus growing patient lists, has made is harder than ever for transplant centers to keep up with the demand.

''We're all losing ground,'' said Gary Hall, a coordinator for the Mid- South Transplant Foundation in Memphis, Tenn.

About 350 Americans are waiting for heart transplants, according to the Organ Procurement and Transplant Network.

Last year, an estimated 1,470 heart transplants were performed in the United States, more than double the number in 1985, according to the government's National Center for Health Services Research.

''Transplantation has become such a successful way of restoring health and maintaining life, (that) more and more hospitals are opening transplant centers,'' said Bob Capito, a coordinator for the Northern California Transplant Bank.

''When a hospital and a group of surgeons make a decision to transplant kidneys, hearts and livers, they're identifying new recipients. They're not taking recipients away'' from other centers, he said.

However, the increased competition for donor hearts has had an effect, officials say.

At Stanford University Medical Center, one of the world's oldest and largest heart transplant centers, four patients have died awaiting new hearts so far this year, said transplant coordinator Jo Maddox. That compares to five such deaths all of last year and three in 1985.

''Hearts that might have been available in the past are now being used locally'' by a half dozen new heart centers on the West Coast, said Marguerite Brown, another transplant coodinator at Stanford.

''It's certainly a reasonable thing,'' she said. ''But for everybody involved in heart transplantation it means if you don't procure donor organs in your immediate area, there are going to be major problems meeting the need.''

The situation seems much the same elsewhere.

At Mid-South, five heart transplant candidates have died during the past six months, compared with no deaths in the preceding six months, said Hall.

The Health Care Financing Administration, for the most part, is demanding experience in exchange for Medicare.

Heart transplant centers must have performed 36 procedures since 1982, including 12 in each of the past two years prior to applying for reimbursement, said Milhorn. The results must be respectable.

''What we're trying to do is to strike a balance between having the standards set high enough that we can be assured Medicare beneficiaries are getting adequate care but at the same time not setting them so high that it wouldn't be do-able except by a handful of centers,'' he said.

''There was a lot of concern we would limit it to some 10 or 12 centers on a geographic basis. We are in effect saying if you meet these criteria, you're in.''

Milhorn doubts the guidelines will shut down many existing centers, which have made a long-term commitment to doing transplants.

Besides, the agency expects only a dozen or so heart transplant patients to qualify annually for Medicare, intended mainly for the elderly, disabled and people with kidney failure.

However, most major insurance companies and about half the states cover heart transplants, and Milhorn said those providers may ''wait to see which way we jump and jump the same way.''