Government lawyers are preparing an unprecedented civil lawsuit to place the 1.7 million-member Teamsters Union under federal control on grounds that it is under the influence of organized crime, it was learned yesterday.

The massive lawsuit, which is being drafted by a team of Justice Department lawyers with help from the FBI and the Labor Department, is aimed at forcing the Teamsters' 21-member executive board -- including union President Jackie Presser -- out of office, sources said.

The civil racketeering action is separate from a Cleveland criminal trial that Presser is facing. Presser's trial, scheduled to start Aug. 10, is not likely to affect the timing of the Teamsters civil suit, which could be filed before the criminal case begins, one source involved in the matter said.

Government officials said that the proposed civil action would be under the Racketeer Influenced and Corrupt Organizations Act. The government already has used the law to place one Teamsters local in New Jersey under court-supervised trusteeship.

The successful suit against Union City, N.J., Local 560, which was controlled by convicted racketeer Anthony (Tony Pro) Provenzano and his brother Salvatore, is the prototype for the proposed suit against the Teamsters Union nationally, sources said.

For years, evidence has mounted in federal courts that the leadership of the Teamsters, the nation's largest trade union, has been close to organized crime figures.

An ongoing criminal trial in New York, in which Mafia boss Anthony (Fat Tony) Salerno and 10 associates are defendants, has featured testimony from former Teamsters president Roy L. Williams and others that Williams' 1981 election and Presser's first election in 1983 were controlled by Salerno through members of the union's executive board.

In addition, convicted Cleveland mobster Angelo A. Lonardo and Williams have testified that Mafia leaders in Chicago and New York ordered loans for Las Vegas casinos from the giant Teamsters Central States Pension Fund in Chicago. That fund has since been placed under court supervision with outside investment advisers.

Statistics compiled by the Labor Department and the President's Commission on Organized Crime list more than 100 local Teamsters officials and consultants in the last five years who have been convicted or are under indictment for embezzlement, mail fraud, bribery, racketeering or for defrauding union health and welfare plans.

An official, who asked not to be identified, said that the lawsuit would include "misfeasance" charges against Teamsters leaders for their alleged failure to root out internal corruption.

Sources said the suit would be filed by Joseph E. diGenova, U.S. attorney for the District of Columbia, who declined to comment.

The suit would be filed in federal District Court. If it succeeds, the court would appoint trustees who would manage the union, replacing its executive board. The trustees would report to the judge, who would have the authority to continue monitoring the union's activities, for as long as he deems necessary, to ensure that it had cleansed itself of criminal elements.

John R. Climaco, general counsel of the Teamsters and Presser's personal defense attorney, refused to comment on the matter.

The move to assert federal control over the giant union would be the latest in a series of turnarounds in the relationship between the administration and the Teamsters -- the only major union to support President Reagan twice.

Attorney General Edwin Meese III has removed himself from matters involving Presser because of contacts he had with him during the 1980 campaign and later.

The pending criminal case against Presser and two associates, international vice president Harold Friedman and Cleveland recording secretary Anthony Hughes, is based on allegations that they siphoned off $700,000 in union funds over 10 years to pay the salaries of Mob-related "ghost employes" who performed no work. All three have pleaded not guilty to the charges against them.