Egyptian President Anwar Sadat, deeply concerned by the turmoil in Iran, has offered to play a major prowestern military role in the Middle East in exchange for the United States equipping his armed forces with billions of dollars of modern weaponry.

Authoritative U.S. sources said Sadat made the proposal to Defense Secretary Harold Brown on Saturday during a lengthy private meeting in Egypt. He unfolded his plan after Egyptian defense officials presented Brown's subordinates with a military shopping list that one source described as involving "billions upon billions of dollars."

According to the sources, the Egyptians are seeking up to 300 F16 fighter-bombers, hundreds of tanks, shortrange tactical missiles and other artillery and thousands of armored personnel carriers and other vehicles.

In return, the sources said, Sadat talked of Egypt, its forces modernized by this equipment. assuming responsibility for ensuring stability in a region stretching from Algeria east to Afghanistan and from the Mediterranean south into sub-Sahara Africa to Somalia or beyond.

Sadat's proposal came on the eve of renewed Egyptian-Israeli peace talks, which resume today at Camp David under the mediation of Secretary of State Cyrus R. Vance. But, although Sadat is known to have told Brown that Egypt will make no more concessions in the peace negotiations, the sources said he stressed to Brown that the requested equipment is not intended for use in conflicts with Israel.

Instead, the sources said, he seemed to be assuming that Egypt's three-decade dispute with Isrel is on the way to resolution and was referring to Egypt's Middle East role following an Egyptian-Israeli peace accord.

In response, the sources added, Brown promised that the Carter administration will consider Sadat's arms requests seriously and without attaching any conditions that there first be a settlement with Israel. Howeve, according to the sources, Brown added that the realities of U.S. politics mean there would be little likelihood of Egypt receiving massive infusions of American weapons unless the Camp David talks lead to a peace treaty.

At present, the only major U.S. weapons commitment to Egypt is for the sale of 50 F5 jet fighters -- a basically short-range, defensive aircraft. By contrast, as part of the same package, Washington is selling 75 of the more sophisticated, longer-range F16s to Israel.

Sadat's armed forces currently are equipped largely with Soviet weapons, but his pipeline to Moscow has been shut off since 1974 following the rupture in his ties to the Soviets. Since then, he has moved progressively toward the West, and, according to the sources, he made clear to Brown his expectation that the United States now will take the lead in reequipping his forces with western arms.

If that is done, the sources said Sadat told Brown, Egypt could make a big contribution toward stabilizing the military balance in the Middle East both through its own strength and through turning much of its present Soviet equipment over to friendly smaller countries in the Middle East and Africa.

In his talks with Brown, the sources noted, Sadat made no secret of his concern that the toppling of the shah of Iran's pro-western government could trigger unrest and turmoil throughout the Middle East. The sources described him as expressing particular concern about future instability emanating from two neighbors of Egypt, Libya and the Sudan.

But, the sources stressed, in outlining his concept of a regional policeman's role for Egypt, Sadat sketched a geographic and strategic sphere of potential activity extending far beyond Egypt's immediate neighbors.

In fact, some of the sources added, he seemed to be offering Egypt as a substitute for Iran on an even grander scale than had been assumed by that country under the shah.