More than two decades after it kicked the Teamsters Union out for not cleansing itself of alleged corruption, the AFL-CIO is trying to bring it back into the federation. The reason: the power of numbers.

With its 2.3 million members, the International Brotherhood of Teamsters is the largest union in the country -- in or outside the labor federation.

Put another way, one of every 10 of the nation's 20.2 million unionized workers is a Teamster.

THE AFL-CIO's 13.6 million members, united with the Teamsters, would give organized labor a powerful coalition for confronting what it perceives as the growing influence of big business on Congress and the regulatory branches of the federal government.

The reunion would bring something for everyone: for the Teamsters, the kind of public legitimacy officials of the scandal-scarred union privately admit they need, and for the federation, added clout and organizing power.

The Teansters' organizing ability is legend. In 1889, when it was originally chartered by the American Federation of Labor, the union was made up of strong, autonomous locals in several large cities. Individual members came from the ranks of the delivery trades large cities. Individual members came from the ranks of the delivery trades -- the haulers of milk, coal, construction equipment, etc.

Now, truckers and haulers make up barely 25 percent of the Teamsters' total membership. The other 75 percent comes from the nation's hospitals and dental offices, police and fire department and a host of other fields with little or no relationship to trucking.

Teamsters affiliates are found in Salisbury, N.C., as well as in New York City and Chicago. They can also be found in the coal fields of the West.

"We'll organize almost anybody that wants to be organized," said Tony Zivalich, a southern regional Teamsters field representative in Boca Raton, Fla.

It is more than a boast. In the right-to-work South, for example,the Teamsters have developed a reputation akin to that of a lawyer who chases ambulances. Firms such as Pittsburgh Plate Glass Industries Inc. which relocated from the north to the south, where labor is cheaper, have become the targets of successful Teamster representation drives.

Similar success eluded the Teamsters in New Orleans last year in efforts to organize that city's police force. But it was something of a Pyrrhic victory for city leaders. The dispute forced the cancellation of the Mardi Gras, something occasioned in the past only by the outbreak of war or epidemics. The city lost millions of dollars in tourist revenue.

The Teamsters have had a standing invitation to rejoin the federation since Lane Kirkland assumed the AFL-CIO presidency in November.The invitation was renewed last month with the unanimous support of the federation's 35-member executive council a the Afl-cio's annual mid-winter meeting in Bal Harbour, Fla.

"I am satisfied that the Teamsters is a bona fide trade union that has been working in the best interest of its members," Kirkland said in announcing the creation of an Afl-cio panel to work out reaffiliation with the union.

Kirkland publicly does not take the Teamsters' organizing clout into account when he speaks of bringing back into the federation the union expelled by Kirkland's predecessor, the late George Meany, in 1957 for refusing to follow AFL-CIO directives to rid itself of alleged "corrupt domination."

Kirkland turns aside suggestions that he is breaking new ground. "There is nothing novel about the idea of unity in the trade union movement. It's ot a new direction we're moving in. We're striving for unity . . . . That is one of the oldest strivings in the trade union movement," he says.

But in the far reaches of the cavernous AFL-CIO headquarters here, there is also the realization that unity without clout is anemic.

Said one AFL-CIO official, commenting on the Teamsters: "They are a big, strong union. No one denies that. With them in a unified labor movement, we'd be better able to fend off some of the attacks on organized labor on the [Capitol] Hill and elsewhere around the country."

That official said there is no substance to speculation the AFL-CIO wants the Teamsters as a possible conservative counterbalance to the more liberal, 1.3-million member United Auto Workers, who have also been invited to rejoin the federation.

Another federation official dismissed as groundless concern that the Teamsters, whose reputation for alleged lawlessness rivals its legendary organizing strength, will sully the image of the federation.

"Despite all of the stories and headlines, most of the people in the Teamsters are like people in any other union -- good, solid, ordinary guys," said the federation official, apparently forgetting that women account for 27 percent of the nation's organized workers.

Still, the negative reputation persists, kept alive partly by a continuing investigation of the Teamsters Central States Health and Welfare Fund, which lost $7 million recent years, allegedly through fraud.

Occasional convictions of Teamsters Leaders, such as that which sent New Jersey Teamsters official Anthony (Tony Pro) Provenzano to jail last year on charges of labor racketeering and conspiracy, also have hurt. And, of course, someone is always bringing up the mysterious 1975 disappearance of former Teamsters President James R. Hoffa.

"That's really unfair," complained a Teamsters spokesman.

"It's mixing apples and oranges. It has nothing to do with what we are today."

Teamsters officials, who have had their reaffiliation panel in place since January, were pleased with Kirkland's remarks. The AFL-CIO president, a widely known, highly respected figure in and outside the labor movement, had publicly declared them ethically fit -- clean enough -- to come home.

However, Teamsters leaders responded publicly with restraint, thanking Kirkland for recognizing their contribution to the labor movement, but saying that "certain things would have to be worked out" before reaffiliation becomes a reality.

Those "certain things" seem mostly technical . For example, one Teamsters spokesman explained, "Our feeling is that there will have to be some kind of a vote on the question. The vote might come from a representative as a whole."

The Teamsters spokesman declined to comment on the probalbe date or to speculate on the outcome of any reaffiliation vote.