Intelligence sources have raised an intriguing possibility: a rapprochement between the United States and Cuba. At first, the suggestion seems farfetched, but normalization of relations with Castro would undercut the Soviets and produce a dramatic international turnaround -- all at a cost to President Reagan. As Richard Nixon's opening to China demonstrated, a Republican in the White House can pull off this kind of political heresy without the cries of "Treason!" that would greet a Democrat.

The whole idea naturally depends more on Castro than on Reagan. My sources tell me he is fed up with his superiors in the Kremlin. While he has undisputed control of his little island and its 9.6 million inhabitants, what he apparently yearns for is the position of Third World leader that was held for many years by Marshal Tito of Yugoslavia.

But Castro has a huge problem. Unlike Tito, who broke with the Kremlin three years after his Soviet-supported victory in Yugoslavia, Castro has slipped increasingly in debt to the Russians as every year goes by. And, what is worse, from his viewpoint, he has been unable to keep his vassalage to the Soviets a secret. Castro is widely perceived in the Third World as little more than a Kremlin stooge.

To a man of Fidel Castro's self-esteem, this well-deserved reputation has apparently become intolerable. He recognizes his folly and is even willing to admit it. Last summer, at the first anniversary celebration of the Nicaraguan revolution, Castro warned the Sandinista leaders not to make the mistake he did by "getting into bed" with the Russians.

What keeps Castro in thrall to the Russians, of course, is the billions in Soviet aid that keeps the mismanaged Cuban economy barely viable. Without the infusion of $10 million a day in aid from Moscow, Castro's government would collapse. Soviet oil fills virtually all of Cuba's energy needs. Two disastrous sugar cane and tobacco harvests in a row have put Cuba hopelessly in debt to the Russians.

But intelligence souces say Castro still sees himself as the champion of the world's oppressed masses. "In opposing Western 'economic imperialism,' the remaining vestiges of European colonialism and white minority regimes of South Africa," a secret State Department report notes, "Castro brings to his mission an almost messianic zeal."

The Cuban dictator still retains his old charisma among Latin America's young militant radicals, who are willing to ignore his dependency on the Soviet Union. He even has a certain amount of respect among more moderate leaders in the hemisphere, who see the main enemy as the military-landowning oligarchs who have oppressed their nations for centuries.

And so far Castro has had no difficulty finding Cuban recruits for his military adventures abroad -- for the pathetic reason that a soldier's pay is not only steady, but an improvement over the misery of life in the city slums or backbreaking work in the sugar-cane fields.

But sources told my associate Bob Sherman that Castro's overseas expeditions are increasingly unpopular at home. Cuban families with sons and husbands fighting and dying in Africa apparently see the foreign campaigns as less an idealistic struggle than an attempt to fulfill Fidel Castro's warning dreams of international power.

And no matter how many Cuban men he sacrifices in Angola and Ethiopia, Castro's hopes of achieving the prestige of Third World ascendancy are doomed as long as he continues to be perceived as a Kremlin lackey. Castro recognizes this, but so far hasn't figured a way out of his dilemma. Maybe an "opening" to the Reagan administration will strike him as worth trying.