The military services are involved in one of their classic arguments with the Defense Department over one of the most treasured of the nation's social programs: the GI bill.

There hasn't been a real GI bill for five years, but substantial pressure is building for one in Congress, with backing from the Pentagon. The battle there is over who would pay for the program, not over the question some people are asking: whether it really is needed as a recruiting incentive.

The secretary's office would like a GI bill that the individual services finance from their own budgets; the services, on the other hand, would like the Veterans' Administration to pick up the tab.

"All the services want the VA to pay for it," said Lawrence J. Korb, assistant defense secretary for manpower, reserve affairs and logistics, but he said the DOD bill will not work that way. It will also include, he said, a requirement that each year's commitment to the educational fund be paid each year. That way the Pentagon would avoid the "unfunded liability" that has occurred in various pension accounts.

The primary justification for a GI Bill is that it would encourage people to join the all-volunteer military. But hard times, improved pay and (the Defense Department thinks) renewed respect for the military uniform have eliminated recruiting problems. For the last two years, the armed forces have met or exceeded their recruiting goals.

Nonetheless, at least four versions of a new GI Bill are floating around Congress, including one that would cost $5 billion a year. "There's a lot of nostalgia value if nothing else," a Capitol Hill source said, referring to the millions of veterans who have gone to college on the GI Bill since the end of World War II.

Only the General Accounting Office is questioning whether such aid is necessary. In a recent report, GAO recommended that Congress pass no GI bill until the Pentagon tests several concepts and reports back.

But that idea is going nowhere. Both DOD and Capitol Hill sources agree that some kind of new GI Bill is probable this year.

Korb said his office "shares the concerns" of the GAO, but "I think we ought to have a GI Bill. It legitimizes military service for many people and appeals to a class of individual we are not always getting." Similar sentiments are expressed on Capitol Hill.

"We are shortest in high-quality people in the combat arms the infantry, the armor and the artillery ," Korb said. A GI Bill promising help with a college education would attract some young people despite the fact they would not leave the service with a transferable skill, he said. Further, he said, "We need a high turnover in the combat arms because youth is important."

The military now has something called the Veterans Educational Assistance Program (VEAP), which is similar to an employe contribution plan. The GI contributes $1, and the Veterans' Administration puts in $2. At the end of a three-year enlistment, the GI would have $8,100 for college. Only 67,800 enlisted personnel are currently taking advantage of VEAP, although all of the 1.5 million young people who have entered service in the past four years were eligible.

The Army is also trying a new program this year called "Ultra-VEAP," which offers up to $20,000 for those who stay in the combat arms for four years. They must also be the kinds of people all the services want: high school graduates with good scores on the Army's tests.

Korb's new GI Bill would cost the Pentagon about $1 billion annually. It would eliminate employe contributions and would allow the services to target educational assistance to skills they especially need, such as infantrymen. An individual could get as much as $8,000 in aid by the end of his enlistment.

One of the problems the GI Bill is supposed to help solve, particularly for the Army, is a congressional requirement that only 20 percent of recruits fall into below-average categories of mental abilities as scored on an entry test.

That was no problem in fiscal 1981, when 82 percent of the Army's recruits were high school graduates and scored well on the tests. But the year before, only half of the recruits had high school diplomas. The year before that, the armed forces recruited only 93 percent of their goal.

The Army has asked Congress for relief from the 20 percent rule, not only because its recruiting history indicates congressional goals will be difficult to meet in the years to come, but also because the size of the military manpower pool is dwindling as the average age of the population increases.

It is not, therefore, an easy issue. "Actually," said Korb, "a GI Bill would probably hurt retention. So we have to be careful."