The Carter administration is giving Iran until Jan. 16, two weeks from today, to accept the latest U.S. hostage-release proposals, which may be withdrawn by the Reagan administration after Inauguration Day, Jan. 20.

Official sources described the Jan. 16 date, which is included in the proposals being taken to Tehran by Algerian emissaries, not as an ultimatum but "simply a fact of life."

Unless Iran accepts the U.S. plan by that date, officials said, there will not be enough time for the outgoing administration to implement the complex proposals for legal and administrative actions concerning Iran's financial assets before Ronald Reagan is sworn in as president at noon on Jan. 20.

These proposals, it was made clear yesterday, call for placement of steadily increasing sums of Iranian assets in an "intermediate" position -- outside the full control of the United States but not yet in the hands of Iran -- as a prelude to release of the 52 Americans.

The Carter adminstration, according to a senior strategist, is determined not to leave the slow-moving negotiations over the hostages in an ambiguous state that limits the options of its successor.

Following this line of thinking, the American proposals should either be accepted and implemented and the hostages on their way to freedom by noon on Jan. 20, or in such a dormant state that Reagan can exercise the option of taking the proposals off the bargaining table in favor of a different approach.

Official emphasis on this point grows out of the demonstrated difficulty of the Iranian authorities to make decisions quickly and their tendency toward 11th-hour action, such as the conditions adopted by the Iranian parliament, or Majlis, on Nov. 2 -- two days before the U.S. presidential election.

State Department officials have recently said that any agreement concluded with Iran by the outgoing administration by Jan. 20 will represent a full-scale commitment of the United States, to be carried over into succeeding administrations. However, proposals remaining on the table but not accepted will be subject to review or withdrawals by the incoming administration, according to State.

High officials of the incoming Reagan administratin have begun to consider ways of handling the 14-month-old hostage crisis in the increasingly likely event that they will inherit it on Inauguration Day, according to sources in the Reagan camp, but no decisions are in sight.

The Reagan team has been closely informed by the Carter administration of the developments in the indirect negotiations with Iran. But Richard V. Allen, who has been designated national security affairs adviser in the Reagan White House, told reporters that the Reagan camp has not been involved in the Carter administration's decisions.

In the face of conflicting reports, the State Department has described as "hypothetical and speculative" various reported figures of sums of Iran's blocked assets that might be quickly returned to Iran or placed in escrow in connection with release of the Americans.

As U.S. officials envision it, Iranian funds could be accumulated in an "intermediate position" such as an "encrow" arrangement supervised by Algeria or another third party. Such an arrangement was "an option" in earlier U.S. proposals to Iran, officials said.

But this has been made explicit and given new emphasis in the most recent U.S. proposals as a means of responding to Iran's demand for tangible "guarantees" that it will get its assets back.

Officials familiar with the details said that no money would be conveyed to Iran until all the hostages are released and that sums to be conveyed to an "intermediate position" as an interim step would be almost impossible to predict with certainty.

"This would be a progressive thing," an official said, with amounts growing in size as loan payments or legal claims were settled under various agreed-upon procedures.

As made clear in earlier U.S. responses to Iran's conditions for release of the hostages, about $2.5 billion in Iranian government assets held by the Federal Reserve Bank of New York would be available to be moved quickly in connection with the hostage settlement.

About $3 billion in Iranian funds on deposit with U.S. banks abroad could be moved relatively soon, officials said, if Iran makes payment of smaller sums owed to these banks.

Additional Iranian funds held in this country could be moved as it was determined that no financial claims by Americans are pending against them or as their movement was permitted by a binding procedure for settlement of the outstanding claims.

On Dec. 19 Iran demanded that the United States deposit $14 billion in the Iranian Central Bank as a "guarantee" that Iranian assets in this country would be returned, and that an additional $10 billion be deposited as a "guarantee" of payment of U.S. assets of the late shah, Mohammad Reza Pahlavi, and close members of his family.

The United States rejected this plan as unreasonable and impossible, and this week formulated a counterproposal in four days of talks, which ended Tuesday, with Algerian emissaries.

The Algerians arrived in Tehran late yesterday to present the new U.S. proposals.