Chicago may have preliminary approval to hold the 1992 World's Fair, but its not going to get the final nod without a fight.

Officials in Miami, arguing that their city's proximity to the terminus of Christopher Columbus' 1492 voyage to the New World makes it better suited than Chicago to celebrate the 500th anniversary of the trip, is mounting a last-ditch effort to win the 1992 fair.

But the lateness of Miami's bid -- and what government sources say is the over-aggressiveness of boosters of Miami's proposal -- may give Chicago the edge. Miami officials say they might have a fair anyway -- and that too could cause problems.

Although Chicago's bid to the Bureau of International Expositions (BIE) has been backed by the U.S. government, President Reagan must still give final U.S. approval to a fair candidate. The approval, expected in late October, will be based on a recommendation by the Commerce Department's Office of International Expositions from applications made by Sept. 1.

Randy Coleman, the lawyer who is president of Miami's Expo 500 committee, was putting the finishing touches on the city's application late last week. Miami wants to have its fair on Virginia Key, an island 2 miles out in the Atlantic Ocean from downtown Miami. Causeways, ferries and a monorail would take visitors to the 370-acre site. Coleman estimates the cost of the project at $600 million to $700 million, and hints that the Walt Disney organization might bring some of its magic to the management of the fair.

George Pratt, director of international exhibitions at the Commerce Department, says both applications will be weighed equally. "If Miami were clearly superior, then the decision would have to be made about going back to the BIE and asking for a change of venue," he says.

But a source close to the situation said Miami's bum's-rush approach to the fair application -- which has included pressure from Florida's Congressional delegation, members of the Organization of American States and public-relations agents -- could hurt Miami's chances.

"The decision will be made on the merits of the application--that's the technical merits," the source said. "They seem to have been going pretty far afield of that process, with going into the political, the international, and the public-relations fields on this thing."

Miami officials might be undaunted by rejection. "I would say fairly definitely we will have one even if Chicago gets it," Coleman said.

That attitude could hurt Miami's chances as well, the source said. And a renegade fair could create some problems for the U.S. government. As a signatory to the BIE, which is essentially an international treaty governing world's fairs, it must "act against the organizers of false expositions or expositions to which participants may be fraudulently attracted," according to BIE law. Just what the government could do, however, is unclear. (The United States was not part of the BIE when New York held its fair in 1964-65 without BIE approval.)

Coleman insists that a non-sanctioned Miami event -- which would probably involve several Latin American countries -- would not run afoul of the rules. "We would not be pretending to have a world's fair," he said. "It would be an international exposition."