WHAT ROLE DOES President Reagan see for American labor unions? None at all, some of his detractors would reply--unfairly. But the real answer may not be much more attractive, if one can judge the president by some of the company he keeps. Last month Mr. Reagan chose, as a forum for a major speech on Central America, the convention of the International Longshoremen's Association, an organization with an unsavory past, to put it in the mildest possible terms. The president heaped rich praise on the union and on its president, Teddy Gleason.

Then there is the matter of the Teamsters Union president, Jackie Presser. The reputation of the Teamsters is a secret to no one: three of its last four presidents have been convicted of serious crimes; some of its leaders have had ties with organized crime; and it has a history of using intimidation and violence. Yet it is something of a favorite of this administration. Mr. Presser has been invited to a state dinner at the White House and he has visited officials frequently in White House offices. Such close contacts may stop now that White House Counsel Fred Fielding has advised top presidential aides to keep Mr. Presser at "arm's length" because he is under investigation by the Labor Department. Will the White House begin to support the trucking deregulation bill, which has been "on hold" because of Teamster opposition?

Why has the Reagan administration been so cozy with the leader of such an unsavory organization? The Teamsters were one of the few labor unions to endorse Mr. Reagan in 1980, and Mr. Presser played a key role in getting that endorsement. So you might say that by courting the Teamsters the administration is just paying off a political debt. But even on that level it's not clear what the Reaganites got--how many Teamster members vote the way the union tells them?--for all that they are giving in return.

Presumably the White House will henceforth keep a greater distance from Mr. Presser. But questions remain. Will investigations of Mr. Presser and the Teamsters proceed on the merits? Is the administration's continued opposition to trucking deregulation a political payoff? And, most important, does former union leader Ronald Reagan really think that labor unions should be run the way Jackie Presser and his associates run the Teamsters?