The Pentagon is studying ways to cut its budget for next year by $8 billion to $11 billion, officials said yesterday.

Despite the unbending public line of President Reagan and Defense Secretary Caspar W. Weinberger that the defense budget cannot be cut, Pentagon budget chiefs have been ordered to assess the impact of a possible cut that size and how it might be made.

The cut would be from $285 billion in total obligational authority that the armed services had been told they could count on. That represents new spending commitments the Pentagon can make in the fiscal year and is different from the amount that actually will be spent. Spending for fiscal 1984 had been projected at $247 billion.

Weinberger's new willingness to consider cuts, officials said, stems from new Reagan administration projections that the federal deficit will be $200 billion in fiscal 1984 and as much as $280 billion by 1988, without spending cuts or tax increases. The president discussed those figures with Cabinet members Tuesday.

Weinberger, in his first two years as defense secretary, was able to fight off efforts by Office of Management and Budget Director David A. Stockman and others to cut the Pentagon budget before submitting it to Congress, though in each year it was cut slightly later.

He still may refuse to budge on the projected total, but he has taken the first step toward cuts by directing Pentagon comptrollers to see how much damage an $11 billion cut would do to Reagan's five-year plan "to rearm America."

In a meeting at the White House shortly before Christmas, Reagan assured the Joint Chiefs of Staff that they would get whatever money they needed to continue the rearmament effort, expected to cost $1.6 trillion over five years.

If Reagan and Weinberger conclude that the fiscal 1984 defense budget must be cut before it goes to Congress this month, in response to demands that defense must share in the economizing, it will be up to the individual services to recommend specific reductions in their spending programs.

"There's going to be a mad scramble around here if we have to cut $8 billion to $11 billion at this late stage," said one defense official, noting that the Pentagon's primary budget leaders have just left office. He referred to Frank C. Carlucci, the Pentagon's detail man, who just left the post of deputy secretary of defense, and Jack R. Borsting, former comptroller.

The military services, if the cut is imposed, will have to cancel hardware programs, stretch them over a longer period of time to reduce spending in any one year or go down in size. They almost certainly would choose to stretch out programs, even though some lost savings from mass production would drive up the price of individual weapons.

Some Pentagon officials contend that going along with White House pleas for cuts in its fiscal 1984 budget would be a losing proposition because whatever figure is submitted to Congress will be slashed further. This has been Weinberger's position in the past.