Washington — The Reagan administration is taking a hard look at Mexico's three-point Central American peace plan to see whether it fits into President Reagan's Caribbean Basin initiatives.
Mexican President Jose Lopez Portillo, offering to serve as a ''communicator, '' last weekend proposed a program to ''dampen down'' tensions in El Salvador and Nicaragua - and to get the United States and Cuba talking again.
So far, the US has little to say, officially, on the subject. President Reagan's speech outlining his Caribbean development plan this week failed to mention the Mexican proposals. And he sounded a hard line on both Cuba and Nicaragua - a tack that was far from what Mexico hoped for.
Yet there is some enthusiasm in the administration for the Lopez Portillo proposals. Mr. Reagan told several journalists the day after his speech that he had just received a letter from President Lopez Portillo on the Mexican initiative. As soon as it is translated, said Mr. Reagan, ''We will have to look at it and study it.''
Moreover, hemisphere diplomats, including officials at the Organization of American States (OAS) are putting considerable pressure on the Reagan administration to study the Mexican proposals carefully.
Hemisphere analysts worry that the turmoil in Central America threatens to throw the region into a conflagration.
Some see Mr. Lopez Portillo's proposals as perhaps the last opportunity to keep Central America from region-wide chaos. The Mexican leader calls for:
* A negotiated settlement of El Salvador's civil war and promises of elections and safeguards to keep the small nation from a Marxist takeover.
* A nonaggression agreement between the US and Nicaragua - involving disarming of Nicaraguan counterrevolutionaries in Honduras, Florida, and California in return for a sharp cutback in the size of the Nicaraguan Army, and guarantees of pluralism and a mixed socialist-capitalist economy.
* Fresh US-Cuba talks aimed at cooling mutual hostilities, with Mexico playing ''a more active role in this context.'' Lopez Portillo hopes for a dialogue between the two countries like that opened last November in Mexico City between Secretary of State Alexander M. Haig Jr. and Cuban Vice-President Carlos Rafael Rodriguez.
Cuba has tentatively accepted Lopez Portillo's proposals. President Fidel Castro declared his willingness ''to offer the fullest guarantees'' that Cuban weaponry will not be used for aggression anywhere in the hemisphere. But in a message to the Mexican President, Dr. Castro asked that the Reagan administration stop what he termed its ''continuous threats'' against Cuba's neighbors in the region - specifically against Nicaragua and the Salvadoran leftist guerrillas.
Officially the US has been reacting coolly to proposed negotiation with Cuba and Nicaragua. But officials indicate Washington is inclined to study the proposals carefully.
The trouble for President Reagan, however, is that he put much, if not most, of the blame for the Central American tensions on Cuba. His Caribbean initiative speech said the US would brook no other Cubas in the area, an implied reference to Nicaragua.
That US hard line on Cuba and Nicaragua is not the approach Mexico had hoped to see.
Mexico's self-interest is as much responsible for the Lopez Portillo proposals as Mexico's concern for its neighbors, some observers say. Mexico worries regional tensions could eventually threaten its own southern borders.
Others suggest the plan may also be a last grandstand play by the President, who leaves office next December, but Mexican sources here reject this suggestion.
''Mexico is genuinely worried about the growing chaos in Central America,'' a Mexican spokesman here says.
OAS officials confirm this view. They suggest that Washington would be well advised to ''let Joe handle it'' - a reference to Mr. Lopez Portillo's first name, Jose.
Mr. Lopez Portillo believes that he and he alone is in a position to serve as a bridge between the US and Cuba because of his close contact with leaders of both countries.