The Veterans Administration may be getting into the artificial insemination business.

Buried in the agency's proposed fiscal 1986 budget is a request to begin paying for medical procedures to help some veterans whose service-connected injuries prevent them from having children. VA officials estimate that 20,000 to 30,000 veterans could be eligible for the new service, which has a projected first-year cost of $2 million.

Robert Putnam, spokesman for the VA's department of medicine and surgery, said the agency would pay for the service, but does not plan to offer it in VA hospitals.

"We would make use of the existing technology in the medical community," he said.

Among those eligible for reimbursement, Putnam said, would be veterans with direct injuries to their sexual organs or those partially paralyzed from multiple sclerosis or spinal cord injuries.

Putnam said the program would cover "any injury that would prevent them from procreating" and that the VA already may have a computer code for such disabilities.

It also would include people suffering from psychosomatic injuries such as "post-traumatic stress, or what in the old days was called shell shock," Putnam said. "There's nothing physically wrong with them. They just can no longer do it." While many injured veterans would be able to impregnate their wives through artificial insemination, Putnam said, the VA would pay for those who are not capable of producing sperm to use commercial sperm banks.

Like most federal benefits, the proposal did not simply appear in the federal budget without some pressure from potential beneficiaries. The Paralyzed Veterans of America, which Putnam said "has a great deal of influence," has been lobbying intensively for the program.

Jack Powell, the group's executive director, said he believes that only 300 to 400 paralyzed veterans would enroll in the program each year. But he said money should not be a factor because "we're talking about making up for a problem that a gentleman encountered in direct service to the nation."

Powell said his group approached the VA a year ago after financing studies which found "that the problem is impotence, not sterility, for many of these folks." He said he still is trying to persuade the VA to pay for in vitro fertilization for a female veteran who cannot have children.

VA officials acknowledge there are many unanswered questions about the program. How will the agency determine who is eligible? Will the government be liable if something goes wrong with the procedure?

Putnam said the VA expects the same proportion of liability problems as with other medical procedures it covers.

In cases where it is unclear whether a veteran's infertility is related to military service, Putnam said, a VA medical board would examine the patient and reach a decision. As for whether the proposed benefit may grow increasingly expensive, he said, "We're working . . . to refine the numbers a little more. We haven't completely sorted this out."