President Reagan will nominate Lt. Gen. William E. Odom, Army intelligence chief and a former assistant Army attache in Moscow, to become director of the National Security Agency, the Pentagon announced yesterday.

If confirmed by the Senate, Odom would succeed Air Force Lt. Gen. Lincoln D. Faurer, who resigned April 1 after a sharp dispute with Defense Secretary Caspar W. Weinberger over cuts the administration made in NSA's fiscal 1986 budget, according to officials in the Pentagon and the intelligence community.

Odom, 52, who taught government at West Point and is considered a hard-liner on the Soviet Union, would be the first Army general since 1969 to head the sprawling intelligence complex headquartered at Fort Meade, Md.

The NSA, the most technologically oriented and secret of the government's intelligence agencies, eavesdrops round the world from planes, ships and satellites to warn the U.S. government about developments.

Longtime acquaintances said Odom has considerable expertise in intelligence techniques but not in managing anything as big and complex as NSA. The agency's secret budget is believed to be at least $10 billion a year with a payroll of about 65,000.

Odom's nomination comes after an extended behind-the-scenes fight that sources said involved not only Weinberger and Faurer but Deputy Defense Secretary William Howard Taft IV and CIA Director William J. Casey.

The NSA director reports to the secretary of defense but also is deeply involved with the director of the Central Intelligence Agency in deciding how to use electronic eavesdropping stations abroad and where to place spy satellites.

Faurer's troubles with Weinberger, sources said, actually stemmed from discussions Faurer had with Taft in late 1984 and early this year at the Defense Resources Board when the Pentagon was deciding how much money should go to NSA in fiscal 1986. Faurer, according to informed sources, protested a proposed slash in funds earmarked for a vast computer complex at Fort Meade.

Stymied by Taft at the Defense Resources Board, sources said, Faurer wrote to Weinberger, detailing his objections to the deletion of a prized part of the NSA's budget. The letter got to the White House, sources said, where it led to Weinberger's being asked questions about the item before he was ready to answer them.

Complicating the budget dispute, officials said, was whether Faurer, a three-star general, should be allowed to stay as NSA director until he retires from the Air Force this August or be replaced at the end of his four-year term April 1. He was appointed in April 1981 for three years and was extended for a fourth year, but not the additional four months to bring him up to his retirement date.

Faurer's budget dispute culminated in his submitting retirement papers in March. A search already was under way for his replacement, according to Pentagon officials. Casey, sources said, was backing Vice Adm. Edward A. Burkhalter, director of the Intelligence Community Staff, for the NSA job. Burkhalter could not be reached for comment.

Odom, who was graduated from the U.S. Military Academy in 1954, taught government from 1966 to 1969, served as an assistant Army attache at the U.S. Embassy in Moscow from 1972 to 1974 and was on the National Security Council under President Carter. Since 1981 he has been Army assistant chief of staff for intelligence.

Acquaintances predicted yesterday that Odom would stay out of the limelight as head of the NSA in contrast to the high profile of such previous directors as Vice Adm. Bobby Ray Inman, who frequently made speeches and developed a broad spectrum of allies in Congress. Odom, a staff officer most of his career, is not given to flamboyance but has a professorial style, complete with pipe.