The Reagan administration is inching toward a new trade and investment program for the Caribbean basin to combat Communist influence in that area while strengthening its ties with North America, according to an administration official.

The program, which was discussed during the visit to Washington last week by Mexican President Jose Lopez Portillo, is far from final, said the trade official, who declined to be identified. Under the plan, the United States, Mexico, Canada and Venezuela would coordinate aid, trade and investment incentives through bilateral agreements with countries in the Caribbean and Central America, the official said.

A key part of the plan would be shifting some funds controlled by the Agency for International Development, the Overseas Private Investment Corp. and other trade-related agencies to the Caribbean project from other areas of the world. Doing this rather than appropriating more money would be consistent with the administration's budget cuts, the official said. But the source of the money hasn't been determined, the official added. Coordinating numerous agencies also would save money and resources as necessitated by administration budget cuts.

Under the plan, the United States, Canada, Mexico, Venezuela and other somewhat-developed countries would establish their own bilateral trade, aid and investment agreements with less-developed Caribbean or Central American countries. Some European governments are being considered for inclusion in the plan, the official said. None of the countries has yet agreed to the proposal.

The Caribbean proposal is part of the administration's plan to strengthen relations with Canada and Mexico, two of this country's largest trading partners. The administration also has been concerned about Communist infiltration of some Caribbean and Central American countries, and one U.S. official said the economic plan could improve America's relations there.

But during discussions here last week, Portillo was said to have insisted that no plan automatically exclude any nation such as Cuba from participating. Mexico has established good relations with Cuba, but the United States has no diplomatic relations with that country and maintains a trade embargo against it.

However, the administration trade official said last week that if Mexico or another country asks Cuba to participate, the United States could do nothing to prevent it. "We can't stop Mexico from doing whatever they want with Cuba, Grenada and Nicaragua" -- all leftist governments -- the official said.

So far as countries participating in bilateral agreements with the United States, "We would not exclude any country but certain countries" such as Cuba and Nicaragua "have excluded themselves by the type of governments they have," the official said.

The program is intended to make the Caribbean countries more stable economically and politically to encourage American investment that could be beneficial both to U.S. exports and the host country, the official said. Under the loose outline discussed last week, foreign aid to the Caribbean basin would be tied somehow to benefits to the United States or the sponsoring country. For example, U.S. officials may require the Caribbean country to guarantee protection for a U.S. firm investing there.

Also under consideration is extending the general system of preferences that allows different goods from certain countries to be imported duty free. The United States also would like to see the Caribbean countries adhere more to multilateral rules of trade.