President Reagan has earmarked $4 billion in his new budget for the U.S. forces that would race to this region to save oil supplies that Western nations depend on, Defense Secretary Caspar W. Weinberger said here tonight.

There are indications, however, that Saudi military officials are reluctant to be identified too closely with the Rapid Deployment Force, a U.S. quick-reaction force originally devised under former president Jimmy Carter.

Declaring that "within the next few years" the Soviets will become dependent on foreign oil, Weinberger said, "The worry is that they would move down through passes above Tehran"--through Iraq and Afghanistan--"to seize the oil fields."

To combat that threat, Weinberger said Reagan intends to spend a big chunk of the $4 billion in his fiscal 1983 budget for the force to buy more fast ships and long-distance cargo planes. Existing Marine and Army units would be deployed to make up the force.

In contrast to the Reagan administration's enthusiasm for the mobile unit, Saudi military officers interviewed here during the past two days stressed that they look upon it with concern.

"Keep out," pleaded one Saudi general in talking about the force's proposed ability to speed to the Persian Gulf and other distant trouble spots around the world. "If you come in, then you will give the Soviets an excuse to come in. We will count on ourselves first, Arab gulf states second and you last."

Another Saudi officer at a dinner sponsored by the Saudi government here told reporters at his table that he and other Saudis consider the United States a greater threat to their oil than the Soviet Union.

Asked tonight if he had heard the same kind of views expressed in his private talks with his Saudi counterpart, Prince Sultan, Weinberger refused to discuss the subject. He said he wanted to stick to budget questions at his first press conference here.

However, Weinberger indicated some sensitivity to the Saudis' reservations about the Rapid Deployment Force by saying it would not be deployed in the Persian Gulf or anywhere else except "at the request and with the consent of the host countries." Also, he stressed that he looks upon the force as a firefighting unit for all parts of the globe, and not just the Persian Gulf and Middle East.

Weinberger arrived here yesterday for three days of discussions with Saudi leaders.