Mario Vazquez Rana, the Mexican newspaper publisher who won the bidding for United Press International, has settled his differences with a losing bidder who threatened to upset his $41 million purchase of the news agency.

The settlement between Vazquez and a consortium led by the Financial News Network was disclosed yesterday at a hearing on the status of the UPI bankruptcy.

Officials familiar with the negotiations refused to discuss the "agreement in principle," but they said it would resolve all the litigation and disputes between Vazquez and FNN. It also would resolve UPI management's dispute with Media News Corp., the holding company for UPI's chief stockholders, who gave up operating control of the company last year, lawyers involved said.

The agreement, which is expected to be completed in the next few days, thus would remove the major obstacle to the sale of UPI. The company filed for protection under Chapter 11 of the federal bankruptcy code in April 1985.

Last fall, Vazquez's bid to buy the company was endorsed by UPI's management, its labor union and a committee of its creditors. FNN, one of the finalists in the bidding, has mounted a furious effort to overturn the bid, appealing a bankruptcy judge's preliminary approval of the sale and filing a $975 million lawsuit against UPI, Vazquez and others involved with the decision.

Although FNN's efforts have been rebuffed in the courts thus far, its continuing fight has delayed disposition of the case. With the agreement announced yesterday, however, a UPI spokesman said the case is "on a fast track" and the company could emerge from bankruptcy by June 10.

George F. Bason, the bankruptcy judge in the District, yesterday reviewed a statement describing terms of the sale and UPI's proposed plan of reorganization, and approved its distribution to creditors. The creditors will vote on the plan, after which the sale proposal will return to the judge for final approval.

Joe Levin, an attorney for FNN, said only that settlement talks have been proceeding sporadically since last December. A report by UPI said sources have said previously that FNN agreed to drop its litigation in return for certain UPI assets.