The first significant shakeup in the White House staff since Jimmy Carter took over the presidency is expected to begin within the next few weeks.

Hamilton Jordan, who is increasingly playing the role of an untitled chief of staff, has been conducting a top-to-bottom review of White House operations, and reportedly is close to a decision on the personnel shifts he had in mind.

It is not known whose replacement Jordan will recommend to the president. But indications are that the shifts are likely to be concentrated at the levels just below that of the top half-dozen assistants, where one official said "we are painfully thin."

Jordan's reappraisal comes at a time when the president is under perhaps the greatest political pressure since taking office, with signs of strain as his staff attempts to cope with simultaneous challenges from the coal strike, the Panama treaties and the energy legislation impasse to the stalled negotiations in the Middle East and the Soviet threats to detente.

Jordan's comments to associates in recent days indicate that the president's principal aide has reached the conclusion, voiced for months by others less influential in the administration, that the White House as presently staffed is not measuring up to the job at hand.

Jordan is known to have discussed possible changes of assignment with several people now on the White House staff, but it could not be learned whether he has approached others outside the executive office complex about joining the staff.

No expansion of the staff is contemplated, it was learned, so there will inevitably have to be dismissals or reassignments of present staff members. Jordan is reported to have told one person he interviewed, "The problem is not quantitative; it's qualitative."

According to several sources, jordan, whose role as the principal Carter staff assistant clearly seems to have survived the recent spate of adverse publicity about his personal life, is moving with an authority in the personnel area which suggests he has a mandate from the president to tighten up operations.

But Carter's personal aversion to difficult personnel decisions is so well known to his longtime associates that some of them are still skeptical that many changes will be made. "He just hates to fire anyone," said one official. Another described Carter as being "as soft on people as he is hard when it comes to money."

Even Rosalynn Carter is reported to have complained to friends that the president cuts her off when she suggests that some members of his staff are inadequate.

But Jordan has told associates that it has become obvious to him, in the course of his work on a variety of major problems, that parts of the White House staff are not performing up to par.

It is not known with any certainty where he has pinpointed those shortcomings. Other in-house critics, influential with the president but lacking Jordan's authority, have focused their criticism on the operations headed by presidential assistants Midge Costanza and Jack H. Watson Jr. and counsel to the president Robert J. Lipshutz.

But all three of those senior aides have special claims on the president's loyalty, and there is no indications that the criticism of them is serious enough to put their jobs in jeopardy.

Costanza, who handles public liaison with a wide variety of outside groups, is the only women on the senior staff, and was an early political backer of the president.

Watson, who handles intergovernmental relations and Cabinet liaison, is a protege of Carter's close friend, Atlanta lawyer Charles H. Kirbo.Lipshutz, another Atlantan, was treasurer of Carter's campaigns for governor and president.

One senior assistant who received a good deal of outside criticism in Carter's first year is clearly highly regarded inside the White House. He is congressional liaison chief Frank Moore. Both Carter and Jordan have gone out of their way to underline their confidence in Moore in recent weeks.

The other three senior staff assistants - press secretary Jody Powell, domestic policy adviser Stuart Eizenstat and national security affairs adviser Zbigniew Brzezinski - are also secure in their posts, although Brzezinski has received significant internal criticism on issues ranging from the last Carter overseas trip to his recent brush with Jewish leaders.

Jordan has given some of the colleagues with whom he has spoken the impression that he is concentrating on moves that might strengthen the second echelon of the White House staff.

"The problem we have," said one of those people, "is that once you get past the top person in too many of these offices, the dropoff in competence is pretty sharp."

The sense that Carter has few aides on whom he can really rely has been heightened in recent weeks by the fact that many major decisions are converging on the president at once. Jordan, Powell and others have been shifting rapidly from the Panama treaties fight to the coal strike to the domestic and international aspects of the Middle East impasse, while trying to keep abreast of less urgent but still important matters at the same time.

"There just aren't enough people around there that they can rely on to do something right the first time," said one administration official who has been recruited as a troubleshooter by the overworked staff.

Jordan's effort to improve the staffing is the latest indication of his expanding White House role - which now can barely be distinguished from that of the traditional chief or staff.

Earlier this year, Carter had designated Jordan as the man he wanted to convene and run regular meetings of the senior staff, and had added him to his weekly national security meetings with Brzezinski, Vice President Mondale and Secretary of State Cyrus R. Vance.