Executives in the offices of the Pentagon's outer "E Ring" are predicting sweeping changes at the top before the year is out, with Defense Secretary Caspar W. Weinberger and Gen. John W. Vessey Jr., chairman of the Joint Chiefs of Staff, among the rumored departures next fall or winter.

Weinberger brushes aside rumors that he will leave his post, saying the time to leave "is when you're tired" and he's not tired. But Pentagon insiders already are speculating about successors, with John G. Tower, former Republican chairman of the Senate Armed Services Committee, and Drew Lewis, transportation secretary from 1981 to 1983, the names most frequently mentioned.

Despite Weinberger's past successes with the Pentagon's budget and his excellent relations with the president, some White House officials contend that the defense secretary has been unbending for too long on the military budget, and thus has become more of a drag than a lift to the administration.

Weinberger's budget strategy has been to build a wide base of funding early in the administration and keep adding to it yearly. This year Congress rebelled. It is well on its way to approving only enough money for the Pentagon to cover inflation in fiscal 1986.

Sen. Sam Nunn (Ga.), ranking Democrat on the Armed Services Committee, is trying to head off the defense secretary on the Pentagon's new five-year spending plan. Nunn is demanding that Weinberger tell Congress by Sept. 15 how the department would apportion money in fiscal 1987-91 under budgets allowing a 3 percent increase and zero growth, after allowing for inflation.

"We're trying to force the Pentagon to come to grips with the budget realities" rather than regarding this year as an aberration and go back to the old funding profile next budget season, Nunn said in an interview. He said that there is not enough money in sight to complete "the $150 billion to $200 billion in new starts" on the weapons program that Congress has already approved, much less take on new ones. Under the austere budgets ahead, Nunn said, the Pentagon will have to cancel programs rather than just stretch them out. Otherwise so few weapons would be produced that the cost of each would rise greatly as the savings from mass production were lost.

Vessey, whose four-year tour ends next June, is said to be anxious to retire rather than accept an extension as chairman of the Joint Chiefs, if Reagan should offer it. Corridor talk in the Pentagon is that Vessey would like to leave this fall. Widely mentioned as successors are Adm. William J. Crowe Jr., commander of the Pacific and Indian Ocean forces, and Adm. James D. Watkins, chief of naval operations.

Vessey, an affable former mud soldier, distrusts the news media and has kept a lower profile than other chairmen in his three years as the president's top military adviser. In meetings with President Reagan, Vessey reportedly enthralls him on occasion with war stories and hears cowboy stories in return.

Other departures expected in the near future are Lawrence J. Korb, the Pentagon's manpower chief, whose office lost many functions in a reorganization, and Air Force Secretary Verne Orr. Russell A. Rourke, assistant secretary for legislative affairs, is being mentioned as the likely successor to Orr.

In contrast to these departures, Robert B. Sims, assistant to the president and deputy press secretary for foreign affairs, will be returning to the Pentagon this month as chief spokesman. He formerly was the Navy's second-ranking public affairs officer, with the rank of captain, but lost out to Commodore Jack A. Garrow in the competition for the top job. Now he will be Garrow's boss as assistant secretary for public affairs. Another irony is that Sims, during one of his last Navy assignments, wrote a book about Pentagon reporters -- several of whom he will now have to face in the Pentagon briefing studio.