The American Ballet Theatre, in the sixth week of a labor dispute with its dancers, is likely to announce on Tuesday the cancellation of its scheduled four-week December season at the Kennedy Center, ABT officials said today.

ABT executive director Herman E. Krawitz said, "Unless there's a miracle in the next 48 to 72 hours, there's no way we're going to the Kennedy Center."

After a 14-hour negotiating session Friday and continued talks Saturday, bargaining was broken off and ABT has informed its dancers that in the absence of a labor agreement, it intends to cancel on Tuesday both its Washington season and its January Miami season. The dancers have been locked out since Sept. 2 and ABT already has canceled its Paris and Boston engagements.

Roger L. Stevens, Kennedy Center chairman, confirmed that if there is no settlement, the Kennedy Center expects the engagement to be canceled Tuesday.

Stevens, who is also a member of ABT's board, said that he expected a replacement would be selected, but declined to discuss what he has in mind. "We'll take care of that" when necessary, he said.

ABT's Krawitz said the ballet company feels it necessary to give the Kennedy Center adequate time to find a replacement attraction.

Frank Smith, leader of the dancers' negotiating committee, said the outlook for ABT's 1982-1983 season in light of the labor dispute is "grim" and that the continued dispute "could be the beginning of the end of ABT."

Smith called on ABT artistic director Mikhail Baryshnikov to join in negotiations -- something Baryshnikov has so far refused to do.

Although neither side would reveal details of the latest offer, sources close to the negotiations said proposals by the dancers and by ABT had been approximately $1.3 million apart over the three-year term of a new contract that both sides have been seeking.

But during the marathon sessions over the weekend, the dancers reportedly substantially reduced some of their demands. Sources say ABT made few concessions during the weekend sessions.

The issue of wages has been close to resolution since the lockout began but the two sides are far apart on other issues such as travel expenses, job security and ABT's proposal for massive fines to dancers who fail to sign in on time for pre-performance preparation.

ABT has canceled Kennedy Center engagements two other times: in December 1979, due to a dispute between the dancers and ABT management, and this spring, due to increased costs and a concern that the Kennedy Center was not promoting its appearance fully.