Senior Carter administration officials believe there is a possibility of reaching an agreement with Iran in the next few days for release of the 52 American hostages, but they are fearful that the complex, time-consuming process required to implement the agreement could cause it to unravel before the captives are freed.

To guard against that danger, authoritative sources said yesterday, the administration now is proposing some new ideas to Tehran that it hopes will leapfrog beyond the weeks and months that would otherwise be required and will, as one source said, "get the hostages out very quickly."

Although the sources refused to discuss details of these new proposals, they said they are being transmitted to Iran through the Algerian envoys acting as intermediaries in the indirect negotiations.

In any case, the sources added, there now appears to be a better hope than seemed the case a few days ago that agreement on the principles and mechanics of a hostage-release plan will be worked out before next Friday's deadline set by President Carter.

That, the sources said, is the case despite the State Department's announcement yesterday that Iran has raised several new questions about U.S. proposals for resolving the 14-month impasse. In another outwardly downbeat note yesterday, the department revealed that Deputy Secretary of State Warren M. Christopher, in a telephone message from Algiers, said that "serious problems continue to exsist between the two sides."

Of principal concern to the Carter administration, the sources said, is that the linchpin of an agreement -- arrangements for transferring part of the estimated $8 to $14 billion in frozen Iranian assets held by the United States -- will take several weeks, or possibly months, to bring to the point that Iran feels sufficiently confident about U.S. faith to let the hostages go.

In the interim, the sources continued, the administration is fearful that an accord of such fragility could fall victim to dangers from two directions after Carter surrenders the presidency to Ronald Reagan on Jan. 20.

On one side, the sources said, is the danger that renewed feuding by Iran's fractious political factions could shatter the consensus that apparently exsists there for resolving the hostage problem and force the Iranian government to back out of the agreement.

On the other side, the sources added, is the fact that the incoming Reagan administration, while well-briefed on the broad outlines of the hostage negotiations, has avoided learning about the fine detail and legal ramifications of the Carter-proposed solution. That means the process of implementation could be delayed even further while the Reagan people bone up on these details -- a situation that could increase the chances for impatience and disruption on the Iranian side.

In addition, sources noted, when the Reagan administration is fully familiar with the admittedly controversial legal aspects of the Carter plan -- particularly those that could give rise to challenges from American corporations and individuals with claims against these assets -- it might decide that there are parts of the agreement with which it is unwilling to comply.

Regan gave a hint of that Thursday when, in the course of a statement generally supportive of the Carter administration's efforts, he warned that he wasn't going to sign "a blank check" underwriting without question any deal made by the outgoing president.

According to the sources, these are the pitfalls that the administration hopes to circumvent through the ideas it now seeks to bring to Iran's consideration. Although the details are secret, they involve assurances to Iran about how the United States intends to fulfill its part of the proposed agreement in terms of transferring the frozen assets in a manner that will convince Tehran that its interests are protected.

The United States is known to have proposed that some portiion of the assets be put in an escrow account under Algiers control. But pursuit of that avenue has been impeded by disagreements between Washington and Tehran about the amount that would go into escrow status, about the degree of responsibility that Algeria is willing to assume and about U.S. insistence that Iran agree to measures for assuring eventual settlement of the claims questions.

The situation began to accelerate Tuesday when Iran, through the Algerian intermediaries in Tehran, raised several questions about U.S. proposals. The United States sent a response via Algiers Tuesday night, but the Algerians did not relay it in full to Tehran because Algerian Foreign Minister Mohammed Benyahia had questions about part of the American reply.

Christopher was sent to Algiers on Wednesday to explain the U.S. position in greater detail. State Department spokesman John Trattner said yesterday that a full U.S. reply to the first set of Iranian questions has been forwarded to Tehran.

But, Trattner added, the Iranians unexpectedly sent a barrage of new questions about the substance of the U.S. proposals to Algiers yesterday. As a result, it was decided that Christopher and his team of State Department advisers would remain in Algiers to provide the answers and keep in touch with the situation. It was when Christopher called the State Department yesterday morning, Trattner said, that he reported continuing "serious problems."

This flurry of activity apparently sparked rumors yesterday in London and Toronto financial markets that the United States was about to transfer as much as $10 billion in escrow to Algeria. The State Department characterized the reports as "rumors" without confirmation and a spokesman for Chase Manhattan Bank in New York denied that Chase was involved in such a transfer, either alone or as part of a consortium of U.S. banks holding some of the frozen Iranian assets.