Efforts to negotiate a settlement of the Justice Department's massive antitrust suit against American Telephone & Telegraph Co. have bogged down, and there is increasing doubt that an agreement will be reached by the March 2 deadline imposed by the judge assigned to the case.

The problems with the complex talks come although top-level representatives for both the government and AT&T told U.S. District Court Judge Harold Greene last month that a "concrete" settlement proposal had been worked out. All that remained was the transformation of that proposal into consent decree language, Greene was told in two conferences.

During a meeting on Jan. 14 with Greene and Gerald Connell, the government's lead attorney in the case, Howard Trienens, AT&T's chief counsel, said "we have a tangible concrete agreement.

"We have no complex or controversial features remaining to be resolved in substance but we do have last-minute technical drafting problems as far as AT&T, and since I do have a judgment section, I have to worry about consistency, which will be a matter of days but will minimize the government's internal problems," Trienens told Greene.

According to a transcript of the meeting released by Greene, Connell also called the proposal "concrete" but noted that the "drafting" and "language problems" look to "be fairly complicated."

But knowledgable sources say that even though both sides have seemed close to agreement since as long ago as April 1980 and those earlier talks had progressed toward settlement since December, sticky issues have made the signing of the pact increasingly doubtful. These issues include the proposed divestiture of one or more local Bell System operating companies and the relationships between the AT&T long-distance operation and the local subsidiaries.

Sources said that even the matter of which operating companies would be divested by AT&T has been in flux since Greene was assured that the settlement terms were "concrete," raising questions about whether the two sides were frank during that conference or whether Trienens in fact was negotiating terms that would be approved by AT&T's board of directors. An AT&T spokesman consistently has noted that settlement terms would require the approval of company management.

Further complicating the issue is the Reagan administration's lack of a top-level Justice Department official to approve the trial staff's work in negotiating a settlement. Assistant Attorney General Sanford Litvack, the Carter administration's antitrust chief, will leave the government early next month, and Reagan has not yet named a replacement.

Both Attorney General William French Smith and Edward Schmults, and deputy attorney general, have disqualified themselves from participating in the settlement procedure. Smith was a member of the board of an AT&T subsidiary, and Schmults' New York law firm did legal work for AT&T.

The Reagan administration reportedly has a list of candidates for the antitrust job. That list is headed by William Baxter, a highly regarded professor at Stanford Law School. But there appear to be at least two other candidates for the job at this point.

Charles Renfrew, the Carter administration's deputy attorney general, told Greene in a letter dated Jan. 29 that the new antitrust chief would review the AT&T case, making any settlement proposal "a top priority" and that review would be completed "as expeditiously as possible." But with Congress apparently not meeting until the week of Feb. 23, Senate Judiciary Committee hearings on the nominee and ultimate confirmation by the full Senate could take place only days before a court-imposed consent deadline.

Two weeks ago, Greene told the parties in a terse order that he would not postpone the case again unless the two parties have filed a consent decree with the court by 4 p.m. March 2. The trial, which Greene delayed at the close of opening arguments Jan. 16, will continue on March 4 if no pact is filed.

Although the case conceivably could be settled even after the presentation of evidence begins, AT&T fears that under federal antitrust laws the statements of witnesses and materials offered in the case could be used in pending and future private suits against AT&T. Hundreds of millions of dollars in antitrust claims could be affected if the trial continues, although the question is filled with legal uncertainties.

Nevertheless, rumors of the contents of the proposed agreement also have set off a massive lobbying campaign by a host of organizations that in one way or another are competitors.

Among the leaders in that lobbying assault have been the Ad Hoc Committee for Competitive Telecommunications, a lobbying group of long-distance-service competitors; the North American Telephone Association, an equipment manufacturing trade group; and the National Cable Television Association.

All have criticized the terms of the settlement, as reported in press accounts. The cable television group, expressing concern about AT&T's potential to provide home information services, said its members oppose "adoption of any settlement not substantially consistent with the relief requested by the [Justice] Department."