An internal Defense Department memorandum recommends that the Army cancel its prized plan to build five light-infantry divisions to help offset some of a projected $250 billion congressional cut in defense budgets over the next five years, defense officials said yesterday.

Army leaders are mobilizing for the kind of budget battle likely to be fought within each of the armed services as they are forced to cut back plans they developed when President Reagan's rearmament program had overwhelming political support.

"We've dug in our heels, and we're going to win," one Army leader said yesterday after noting that the light divisions -- four active and one reserve -- had been recommended for the chopping block by the Pentagon's manpower office, headed by Lawrence J. Korb.

Gen. John A. Wickham Jr., Army chief of staff, has championed the light divisions.

"Wickham went ballistic when he heard about the recommendation," one Pentagon executive said in recalling the general's reaction to the attack on his new design for the Army.

Whether to forgo spending millions of dollars to build facilities for light divisions composed of people already in uniform is one of many issues to be thrashed out soon within the Pentagon and in Congress as the fiscal 1986 budget is revised in light of congressional cuts and the new five-year defense plan is designed.

The Defense Resources Board, composed of Pentagon civilian and military leaders, including heads of unified commands, is expected to address the future of light divisions in a budget meeting late this month. Neither Defense Secretary Caspar W. Weinberger nor Deputy Defense Secretary William Howard Taft IV has addressed the proposal to forgo the divisions, Pentagon officials said.

Although it is too early to know precisely how much money the Pentagon could lose through congressional budget cuts, one internal projection puts the potential loss at $250 billion for fiscal years 1986 through 1990 and $300 billion through fiscal 1991.

This year, Reagan sought a 6 percent real increase in his fiscal 1986 defense budget, but the Senate has voted only enough extra money to cover inflation while the House has approved an outright freeze at the fiscal 1985 level.

Sen. Sam Nunn (D-Ga.) has inserted into the defense authorization bill a requirement that the Pentagon show Congress how it would apportion the money over the next five years under a budget allowing for no growth and a second one allowing 3 percent annual increases above inflation.

The Army's light divisions make an inviting target for budget cutters because facilities needed for some of them have not been built. But the two most expensive complexes would be built in the states of powerful lawmakers expected to fight hard to protect them.

The Army has estimated that it would cost $395 million to put a light division in Alaska, home state of Republican Sen. Ted Stevens, chairman of the Senate Appropriations subcommittee on defense, and $1.2 billion for one at Fort Drum, N.Y., home ground of Rep. Samuel S. Stratton (D-N.Y.), a senior member of the House Armed Services Committee.

Army officials say, however, that much of that money would have to be spent even if the light divisions are not formed, because of improvements needed at both sites. That would lower the net cost to about $70 million in operational costs for Alaska and about $400 million for Fort Drum, they said.

The two other active light divisions would use existing facilities at Fort Ord, Calif., and in Hawaii, while the reserve light division would be headquartered at Fort Belvoir, an existing complex.

Besides the cost issue, some military professionals have questioned the value of light divisions pitted against heavily armored Soviet forces. Wickham and his allies contend that a 10,000-member light division's mobility and firepower, compared with the 16,000 troops in a regular division, make it ideal for confronting threats in distant places.

Budget cutbacks will force the other services to forgo new programs and stretch out or cancel existing ones. Some Pentagon executives struggling with ways to make big savings said that the Navy's shipbuilding budget may have to be trimmed and that the future of the Air Force's Stealth bomber may be readdressed.

Several Pentagon officials said Taft was being overly optimistic when he told the services this spring to plan on real increases of 3 percent in fiscal 1987, 5 percent in 1988, 4 percent in 1989, 5 percent in 1990 and 3 percent in 1991.

If this year's congressional budget-cutting mood lasts, as appears likely, the services would have to scale back ambitious plans only partially executed in Reagan's first term.