United Press International asked a federal bankruptcy judge yesterday for permission to file a plan of reorganization that calls for the sale of the financially strapped news agency to Mexican newpaper publisher Mario Vazquez Rana.

Vazquez's $41 million bid for the company was endorsed last fall by UPI's management, the union representing its workers and a committee of its creditors. And UPI's lawyers have spent several months preparing a formal plan describing the terms of the sale and how the agency's debts would be paid off.

"The filing of the plan of reorganization is another significant and timely step toward the completion of bankruptcy proceedings and the sale of UPI," said Luis Nogales, UPI's chairman.

UPI's chief stockholders and one of the losing bidders, a consortium headed by the Financial News Network, have furiously sought to derail the sale, but their efforts have been rebuffed in the courts.

Yesterday, the chief stockholders, Douglas Ruhe and William Geissler, tried again when their lawyer argued that UPI management does not have the authority, without their okay, to file the plan of reorganization.

A court hearing on that argument is scheduled next week. If the argument is denied -- as UPI lawyers expect -- the bankruptcy petition will be filed, clearing the way for the news agency's emergence from bankruptcy proceedings this summer. The plan is first expected to be sent to creditors for their approval.

UPI filed for protection last April under Chapter 11 of the federal bankruptcy code after suffering massive financial losses for years.

As part of the reorganization, Vazquez will provide $15 million in working capital for UPI. Meanwhile, the wire service's large, unsecured creditors would receive about $9.5 million, or about 40 cents on the dollar, as well as 1 million shares of UPI common stock. Small creditors would be paid in full.

Vazquez has also reached an agreement with the Wire Service Guild to keep wages at their current levels through 1987. Moreover, he has promised to institute a profit-sharing programs for UPI employes, to seek to bring wages in line with those of other news services as soon as the successful operation of UPI permits and to seek court permission to pay $500,000 to Brian M. Freeman, an investment banker who helped the guild negotiate the deal.