In its first test in the tricky international politics of the Mideast, the Reagan administration is considering a compromise that would let it sell Saudia Arbia sophisticated additional equipment for its F15 jet fighters without offending the Israelis. It would satisfy at least some Saudi demands while at the same time giving Israel a new infusion of American arms on exceptionally favorable financial terms.

The F15 question -- the Saudis want new fuel tanks and bomb racks that would increase the range and firepower of the fighters the United States sold them several years ago -- is a metaphor for the Arab-Israeli problem generally. Although they stand on opposite sides of a continuing conflict, both Israel and Saudi Arabia are major allies of crucial importance to U.S. policy goals in the Middle East.

The United States is committed to keeping Israel secure and the same time active in the Mideast peace process, while also helping to keep the region's oil-producing states led by Saudi yarbia safe from radical influences and in a pro-Western frame of mind.

On the F15 issue, according to reliable diplomatic sources, both sides have now made their arguments to Secretary of State Alexander M. Haig Jr., and, although further exploration and negotiation will be required, the administration tentatively believes there is enough flexibility, particularly on the Israeli side, to permit a compromise.

Israel, while clearly preferring that Saudi Arbia not get the equipment, is understood to have informed Haig that it understands the administration has a problem and that it might be willing to cooperate if the United States will provide it in turn with additional planes and other weaponry. Israel says it will need these to redeploy its defense forces to guard against the potential threat posed by the Saudi jets.

However, because of their current financial problems, the Israelis also are known to have stressed that they would require special U.S. financial assistance to pay for the extra American arms. In conveying their position, the Israelis were vague about precisely what they want Washington to do, but the inference drawn by U.S. officials is that Israel expects that any increased military aid essentially would be a gift.

On the other side, the Saudis are known to be pressing with increasing impatience for a decision on their request to add multiple-ejection bomb racks and extra-large wing fuel tanks to the 60 F15s ordered from the United States in 1978. To underscore the importance they attach to the matter, the Saudis have made clear that if Washington disappoints them, they are prepared to jettison their special relationship with this country and take their arms shopping list elsewhere.

The administration's desire to prevent such a breach with America's principal oil supplier was stressed by Defense Secretary Caspar W. Weinberger at his Feb. 3 press conference when he described Saudi Arbia's defense problems at a time of increasing violence and instabililty in the Persian Gulf region and said, "We want to do everything we can to assist them in providing the additional security that they need.

Although Haig has not spoken out so explicitly in public, he is known to share the view that a decision acceptable to the Saudis must be made very quickly. However, the administration also must take into account the fact that Israel's concern about increasing the range and offensive capability of the Saudi planes could lead to a bruising fight with Israel's supporters in Congress and cause Israel to back away from efforts to expand the Mideast peace process.

The F15 is the most sophisticated fighter plane in the U.S. arsenal. When former president Carter agreed to sell the F15s to Saudi Arbia, then-defense secretary Harold Brown met objections from pro-Israeli senators with the assurance that the jets, whose delivery is scheduled to begin in 1982, would be purely for defensive purposes and would not have the additional equipment that would enable them ever to be used against Israel.

When it became known early last year that the Saudis wanted to enlarge the deal to include mulitple bomb racks and large fuel tanks, the Carter administration ran into a storm of opposition from Congress, where lawmakers contended such a move would violate the assurance given by Brown.

Carter's tactic was to delay a decision until after last November's presidential election. But, in an effort to woo Jewish voters, Carter just before the election reaffirmed Brown's assurance to the extent of ruling out the sale of the bomb racks requested by the Saudis.

Now, with the election over and the Saudis pressing again, the new administration clearly is disposed, for diplomatic and strategic reasons, to give them what they want -- or at least enough to keep Saudi Arbia from turning to another country. France recently completed a $3.4 billion arms deal with the kingdom and would like to supplant U.S. influence there.

Although the final say would rest with President Reagan, top-ranking State Department and Pentagon policymakers are known to consider the matter so important that, if necessary, they would be willilng to risk a fight with pro-Israeli forces in Congress. Under U.S. law, the Saudi sale would be blocked if both House and Senate voted against it.

No formal soundings of congressional sentiment have been made yet. But the administration is known to believe that the new Republican majority in the Senate, if forced to make a choice, would support the president by upholding the sale.

The Israelis, having made their own nose count, apparently have reached the same conclusion. That, coupled with Israel's desire to avoid an acrimonious fight with Reagan at the outset of his administration, appears to underlie the flexibility and desire for accommodation in the position stated to Haig.

In addition to increased military aid, the Israelis also are understood to want some diplomatic help from Washington. In particular, they want the administration to take a firm stance against the effort of the European Economic Community, under the leadership of France and Britain, to inject itself into the Mideast peace process with an initiative that would make the Palestine Liberation Organization a party to future negotiations.

So far, the administration has not responded to the Israeli proposals. However, reliable sources say that State and Pentagon planners are very interested in pursuing them further to get a better idea of precisely what Israel would want in the way of hardware and how much it would cost.

According to the sources, if the Israeli requests are within bounds that don't cause major shift of the Middle East arms balance or carry a price tag that would be difficult to justify under Reagan's call for budget austerity, the administration, backed up by Congress, very likely would seize on the idea as a cheap price to pay for getting out of the squeeze in which the F15 controversy has put U.S. Mideast policy.