The United States is near an agreement that will ease controls over the sale of high technology to India as the first tangible sign of a Reagan administration initiative to smooth relations with that giant democracy.

The two nations are expected to sign a memorandum of understanding on high technology sales this week in New Delhi after reaching a surprisingly quick accommodation following a visit to India earlier this month by team from the State and Commerce departments, administration and Indian sources said yesterday.

Although small points still are being ironed out, sources said U.S. Ambassador Harry G. Barnes Jr. received authority over the weekend to sign the memorandum detailing steps the Indian government will take to prevent the diversion to the Soviet bloc of the U.S. high technology products it buys that have potential military application. Indian officials here said the agreement has not yet received full approval from their government, though the signing is expected today or Wednesday.

The agreement has been given a high priority by the government of Indian Prime Minister Rajiv Gandhi, a former airline pilot who is so fascinated by new technology that one of his nicknames is "Computerji." ["Ji" is an honorific often added to names in India.]

Indian efforts to gain easier access to American high technology were begun by his mother, Prime Minister Indira Gandhi, who was assassinated on Oct. 30, and received a major push by India's new ambassador in Washington, K. Shankar Bajpai.

These moves on the part of New Delhi coincided with President Reagan's decision last month to try to improve relations. As one of the first steps, the president authorized new talks designed to break the logjam over sales of high technology to India.

India had been seeking ways to get off a Reagan administration blacklist of countries that were considered likely to allow the diversion of high technology to the Soviet bloc because of their lack of controls. Being on the list subjected India to special controls that made it harder to gain access to the powerful comuters and other high technology products it wanted to help develop its industrial base.

India was upset by its inclusion on that list, arguing there was no evidence that U.S. high technology had been shipped through India, while other countries -- including Austria, Sweden, Norway and South Africa -- had been implicated as way stations in the movement of powerful U.S. computers to the Soviet Union and its Eastern European allies.

The issue of selling India high technology was complicated more by its lack of controls over the possible resale of the computers to Eastern-bloc nations than by its close military-supply relationship with the Soviet Union, sources said.

A further complication, though, came from American laws that limit sales of technology that could be used in India's nuclear program because of its refusal to sign the nuclear nonproliferation treaty or to allow international inspection of all its atomic facilities.

Administration sources said that the Defense Department initially opposed the high technology agreement, but relented after the Indians agreed that some physical inspection of their high technology facilities would not violate their national sovereignty.

Some administration officials expressed concern over whether India will be able to implement the controls it has agreed to, but others argued that any diversion of sensitive technology would cloud India's chances to make further purchases.

India, furthermore, showed that it could get from other countries technology similar to what it wants from the United States. India was able to buy two high-speed computers from Norway for its nuclear program after it was denied access to U.S. products, the magazine India Today reported.