A meeting today between President Reagan and his arms control negotiator, Paul H. Nitze, will bring together two crafty septuagenarians at center stage in a high-stakes drama rapidly unfolding in Washington, Moscow and the capitals of western Europe.

For Nitze, 76, the meeting will be an opportunity to gauge the president's feelings on arms control and the intensity of his interest in achieving an agreement with the Soviet Union to eliminate hundreds of Soviet medium-range nuclear-tipped missiles aimed at western Europe before the first of hundreds of new American missiles arrive on the Continent later this year.

For Reagan, who will be 72 next week, the meeting provides an opportunity to hear a candid assessment of the negotiations directly from the most experienced official.

Nitze, a conservative Democrat who has served virtually every administration since that of Franklin D. Roosevelt, is a highly respected figure whose role in the negotiations has become even more important since Reagan fired Nitze's boss, Eugene V. Rostow, as director of the U.S. Arms Control and Disarmament Agency last week.

Nitze is known to accept that Reagan really does want an agreement. And Nitze knows that if he resigned, which he has no intention of doing, it could wreck the negotiations and lose the support of the western European allies for the U.S. missile deployment. But he also is at a stage in life, his friends said, when he does not want to be a puppet in negotiations preordained to failure.

Officially, Reagan is to give Nitze final instructions before he returns to Geneva for the next round of negotiations. But it has been clear from administration statements in recent weeks that Nitze's instructions will be to stick to Reagan's "zero-option" proposal for getting rid of all missiles on both sides while probing for signs that Moscow might offer much greater reductions than it has so far.

Officials said it is possible that some vagueness could emerge during the White House session that might give Nitze a slightly broader charter.

What Nitze is known to be concerned about is the ability of West Germany, in particular, as well as Italy and Britain to carry out the planned U.S. missile deployment if there is no agreement with the Soviets.

Nitze's worry is that simply continuing to repeat without any sign of flexibility the zero-option proposal, which Moscow has rejected, will add to the prospect that the NATO alliance could wind up with no missiles and no agreement.

Thus, while Nitze supports zero-option as the ideal solution, he also has counseled privately, below the presidential level, for more flexibility to reach a compromise that would ease the political burden in western Europe while maintaining an acceptable military balance.

For the moment, there is not likely to be any shift in the U.S. position until at least after the West German elections on March 6. If the conservative government in Bonn, which backs the Reagan position, is returned to office, this presumably would help convince Moscow that the West is determined to field the missiles unless the Soviets offer a better deal.

What this amounts to is a potentially deadly international game of chicken, which will become intense sometime later this year. Meanwhile, a battle is being fought for public opinion.

On the stage with Reagan and Nitze is the new Soviet leader, Yuri V. Andropov, 68. He is, by all accounts, playing a shrewd role. Portraying himself as the compromiser, Andropov offers proposals that all western leaders have termed unacceptable as they now stand but which have the potential of splitting the western European public from the United States.

At the same time, his foreign minister warns West Germans that following Reagan's lead could mean the nuclear abyss.

Another factor complicating the negotiations is the approach of the 1984 presidential election campaign. The Soviets must be mulling whether Reagan will run again.

Should they wait for a better deal from the Democrats or bargain with Reagan, who can get an arms agreement through Congress? Would Moscow, by agreeing to a deal later this year, when the American missile deployment is to begin in western Europe and the presidential campaign is under way, help Reagan get reelected?