President Reagan has approved the draft of a personal reply to Soviet leader Mikhail Gorbachev in which he expresses willingness to negotiate on all aspects of nuclear arms control raised by recent Soviet proposals, senior administration officials said yesterday.

Reagan's proposed reply could open the way to negotiation on Soviet proposals to tighten language in the 1972 Antiballistic Missile Treaty that affects testing and development, and possibly delay for several years the deployment of a U.S. "Star Wars" missile defense system, an official said.

Such a negotiation, however, would not include research. The president has consistently said he would not bargain away research involved in his Strategic Defense Initiative.

Sources said that Reagan signed off Friday on the draft of a "comprehensive reply" to a letter received from Gorbachev June 23 and to proposals presented by the Soviets in the last round of the Geneva arms talks. The sources said Reagan's draft letter deals with a wide range of issues, including a 50 percent reduction in strategic arms, a compromise on limiting medium-range nuclear missiles in Europe and various regional issues, among them Central America and Afghanistan.

Officials said that, while there was tentative agreement on the wording of the letter to Gorbachev, the State Department and the Pentagon remain at odds on how far the president should go toward what has been called "a grand compromise," in which deep cuts in the superpowers' nuclear arsenals would be traded for a possible delay of several years in the deployment of any missile defense system.

The draft reply is considered so sensitive that it was shown to only four persons, all of whom have had a hand in pulling it together, the sources said. They are Secretary of State George P. Shultz, Defense Secretary Caspar W. Weinberger, national security affairs adviser John M. Poindexter and White House chief of staff Donald T. Regan.

But the sources said that two U.S. ambassadors, Paul H. Nitze and Edward L. Rowny, will brief U.S. allies this week on the "thrust of the message" and that Reagan will not approve a final draft of the letter until he receives a report on their consultations.

Nitze left yesterday to brief European allies, and Rowny is scheduled to depart today to brief the Canadian government and Asian allies.

The administration is sensitive to the reaction of the allies, one official said, because of the furor surrounding the president's May 27 statement that he would no longer be bound by the limits of the SALT II arms treaty.

Before that statement Nitze and Rowny had told the allies that the United States would remain within the treaty limits on nuclear missiles by dismantling two old Poseidon submarines. Reagan did this as promised, but also said in the May 27 statement that the United States was prepared to exceed the SALT II limits later this year because of repeated Soviet violations of the unratified treaty.

Allies complained they were not informed in advance about this part of the decision, which was reached after Nitze and Rowny returned from their briefings.

Officials said yesterday that Reagan took seriously Soviet proposals to reduce substantially their offensive nuclear arsenals and that he was convinced that Gorbachev wanted realistic bargaining when the superpowers resume nuclear arms talks in Geneva in mid-September. They said they expect that Reagan's reply to Gorbachev, scheduled to be sent before the end of the month, will give impetus to these negotiations and to a meeting between Shultz and Soviet Foreign Minister Eduard Shevardnadze, which is expected to occur in New York in late September.

If Soviet reaction to Reagan's letter is favorable, officials said that it is likely that the two superpower leaders would agree to hold a summit in Washington before the end of the year.

The Soviets have tied the deep reductions in strategic arms to an agreement from the United States that it will continue to adhere to the 1972 ABM treaty for 15 years or more. U.S. officials consider the Soviet time period too long, with some favoring a five- or six-year period as part of a counterproposal.

The treaty now permits a nation to withdraw after giving six months' notice, and the Soviets want Washington to agree to disregard this provision.

Shultz is said to consider this idea a promising one, while Weinberger has been reluctant to agree to any advance limitations on SDI or deployment of a system emerging from SDI research.

One proposal under discussion within the administration calls for verified staged reductions in nuclear arsenals tied to a missile defense deployment schedule that presumably could be accelerated if there were violations of the agreement.

In his weekly radio speech on June 12 the president said, "And when we talk about negotiations, let's be clear. Our SDI research is not a bargaining chip." Only the week before a spokesman had quoted Reagan as saying "SDI was not a bargaining chip," without adding the qualifying word "research."

In the Geneva talks, the Soviets have called for a total ban on the U.S. SDI program, including research, despite U.S. charges that they are also are engaged in missile defense research. But Soviet statements outside the negotiating room -- including one last year by Gorbachev -- have indicated an acceptance of missile defense programs that are confined to laboratory research. Both sides acknowledge it would be virtually impossible to verify a ban on such research.

Among other ideas being discussed as responses to the Soviet proposals in both the Pentagon and State Department is a change in the current U.S. provision to ban all strategic mobile missiles. Officials are considering substituting a cap on the number of such missiles each side could deploy and also limiting their deployment to specified geographic areas so their numbers could be more easily verified.

The White House has kept a tight hold on the details of the latest draft of Reagan's response to Gorbachev.

One official who had seen earlier drafts yesterday would not speculate on what the final one contains. He said the FBI is investigating the alleged leak in the July 17 New York Times of one draft provision to link reductions in the number of underground nuclear weapons tests to reductions in strategic weapons.

Attempts last week to verify that such an idea was being considered were unsuccessful, and yesterday The Times reported that the proposal had been dropped from the final draft.