Campaign putdowns to the contrary, Ronald Reagan has quietly signaled his readiness as president to preserve and promote Jimmy Carter's cherished and controversial Camp David "Framework for Peace" in the Middle East.

Nothing official, of course. Reagan, in this as in other transition business, has remained true to his pledge not to intrude upon presidential prerogatives. But indirectly, by discreet word of mouth through his top foreign policy transition aide, Richard Allen, to Carter's middle East negotiator, Sol Linowitz, and on to the Israeli negotiators, Reagan has sent word that there will be a "continuum" in the Camp David peace process after Jan. 20.

The practical effect of this quiet collaboration between the incoming and outgoing presidents is impossible to predict. Just to begin with it is far from clear whether Egypt's President Sadat, third man in the Camp David triumvirate, is much interested in trying to advance the "peace process" until after the American change of command.

But what is clear, both from Begin's public position and from his much more explicit and emphatic private statements, is that the Israeli prime minister is eager to force the pace. The reassurances from the Reagan transition team were solicited by the Carter administration only after it became evident that Begin, as one American official puts it, was "obviously nervous and uneasy" about the fate of Camp David when Reagan takes over.

Publicly, Begin has found more than one occasion to stress that the Camp David treaty is "an international agreement" -- not something to be lightly tossed aside. In his meeting with Carter, he stressed that it is "an agreement between governments," not presidents.

Even more indicative to the American negotiators is the significant progress that has been made in recent weeks on the current, second phase of the Camp David "peace process": the so-called autonomy talks for a limited form of self-government for the Palestinians on the West Bank and in Gaza.

Israeli officials vigorously deny for the record any concessions from their side. But Americans in a position to know report that there have been important new concessions on critical issues having to do with Israeli policy on West Bank settlements after autonomy has been granted, on matters having to do with land and water rights and security arrangements.

There's also been some flexibility on the Egyptian side. "We are a lot further along than you might suppose," one negotiator reports.

True, critical issues remain to be solved. But the clear impression that emerges from just about everything Begin is saying, and doing, is of a geniune effort, with strong encouragement and active participation by the Carter administration, to move the autonomy negotiations well past the point of no return before Jimmy Carter leaves office.

There's talk of the possibility, admittedly remote, of sort of interim "understanding" before the end of the year, leaving a final agreement to the Reagan administration. The suggestion has even been made that Begin, Sadat and Carter could conceivably seal a deal at the summit before Inauguration Day, though that strikes most of the participants as even more remote.

A likelier outcome, if all goes well, would be a unilateral progress report by President Carter by the end of the year, setting forth what has been accomplished and identifying what remains to be done, with at least tacit confirmation from Begin and Sadat. The point would be for the Carter administration to nail down as much agreement as possible before its time runs out.

Pride of authorship is plainly part of it for Carter, because Camp David stands as perhaps his most memorable legacy. But apparently for Begin as well.The autonomy concept for the West Bank he said on "Meet the Press," is "our original idea. It is not American or an Egyptian idea." Intimates say he "wants to show a skeptical world that it will work. He sees peace with Egypt as a historical event. He is ready to go ahead -- not just ready, but anxious."

And there's something else at stake for Begin: next year's election campaign. Israel's inflation-ridden economy will be, as one Israeli puts it, "the number one, two and three issue." Begin's extreme vulnerability was evidenced by the narrow margin by which he survived the latest no-confidence vote in the Knesset. So why not run on war and peace?

Whether this will work any better for Menachem Begin than it did for Jimmy Carter is anybody's guess. But if that's what Begin (which is to say Israel) wants, Reagan is apparently ready to help. The president-elect's devotion to Israel's desires -- as distinct from his previously recorded disenchantment with Camp David -- is intense.

Repeatedly pronounced dead by the Europeans and other detractors, the Camp David Framework for Peace may yet succomb to the hostility of most of the Arab world, or to its own infirmities. But from all the available evidence, it is still very much alive.