Prime Minister Indira Gandhi has signaled that she is willing to put aside differences with the Reagan administration and take a conciliatory position at this week's economic summit between the leaders of 14 developing and eight industrialized nations.

India considers Reagan's views on the economic problems of the Third World unrealistic and not in tune with the real needs of poor countries.

Nevertheless, Gandhi said in an interview with three American correspondents last week, "There should be a beginning of a dialogue" at Cancun, Mexico.

"It seems to us the developing world that the door is closed," she said. "It should be opened. It is something that is bound to take time but a beginning should be made."

Gandhi said she hopes to use her first meeting with Reagan, set for Wednesday, to tell him about the problems of developing nations.

"The main purpose of such a conference is to try to get a deeper understanding of people's and countries' thinking and why they think that way," she said.

Asked how she expects her first meeting with the American president to go, she replied, "There is no reason why it should not go well."

The Indian leader put major responsibility on Reagan for the success or failure of the summit Thursday and Friday. "Much depends on your president," Gandhi said.

"In this whole scenario, the developed countries have to play a key role, most of them will be guided by what the president thinks."

India and China are considered the leaders of the poorer nations of the South represented at the meeting. Apart from the United States, participating for the industrialized North are Britain, Japan, West Germany, France, Canada, Sweden and Austria.

Gandhi appeared to agree with Reagan that freer trade between nations is a key factor in improving the economies of the poorer nations, but she gave no indication that she is ready to lift India's import barriers, which are among the most stringent in the world.

She appeared willing, however, to compromise on proposals that have wide support among the underdeveloped nations as well as some of the industrialized countries, but which are opposed by Reagan.

These include "global negotiations" in which all the nations of the world would thrash out the problems of the developing world, probably under United Nations auspices. The Reagan administration believes that approach leads to confrontations with no hope of progress.

Although she has long supported the concept of global negotiations, Gandhi indicated that she would accept a different type of forum as long as the aim remains the same.

Similarly, she said she is willing "if someone has a better idea" to reconsider her support of an energy affiliate to the World Bank to help developing nations finance the crushing costs of oil and gas explorations.

This idea was first floated by the Carter administration, but opposed by the Reagan administration. Reagan said oil and gas exploration should be left to the private oil companies instead of governments with World Bank financing.

The view that free enterprise and private capital provide the best path for developing nations runs counter to India's economic principles. While India has a mixed economy, with about half of it in private hands, there is a heavy overlay of planning and government regulation. Furthermore, most of the World Bank funds go to the government sector, not private enterprises, as the Reagan administration would prefer.

India could be squeezed badly economically if international aid organizations such as the World Bank and International Monetary Fund adopt the Reagan bias toward free enterprise. Over the years, India has been the largest recipient of foreign aid in the world.

Along with most of the rest of the developing world, India would like increased contributions from the industrialized nations to multilateral institutions. The United States, the largest contributor to the World Bank and IMF, opposes any increases, and there are indications it favors a cutback.

Of even greater concern here, however, is the possibility that Washington will try to punish India for its strong and vocal opposition to U.S. policies in Afghanistan and the Indian Ocean-Persian Gulf regions.

Relations between India and the United States have sunk to a new low over the Reagan administration's plan to rearm Pakistan as the eastern anchor of a "strategic consensus" to protect the oil-rich Persian Gulf against Soviet expansionism.

One Western economic expert here suggested that India would play a conciliatory role at Cancun to ensure that it does not rile the Reagan administration further before the expected Nov. 9 vote on its $120 million IMF loan request.