Mexican newspaper publisher Mario Vazquez Rana yesterday threatened to withdraw his $41 million offer for United Press International unless a federal bankruptcy judge approves a preliminary sale agreement with the news service.

Vazquez attorney Leslie Nicholson told Judge George F. Bason that the court's failure to approve the preliminary agreement would do "incalculable damage to UPI." Vazquez and Houston financier Joe Russo agreed to purchase UPI last month.

UPI also has asked Bason to approve a preliminary sale agreement between the company and Vazquez. Failure to approve the request, Nicholson said, "will be devastating to existing employes and customers and will do incalculable damage to UPI."

The marathon bankruptcy court session began Friday and was expected to last late into the night Sunday as lawyers for Financial News Network, the consortium of rival investors, attempted to overturn the Vazquez-Russo deal.

The preliminary sale agreement called for Vazquez to replace Luis Nogales as UPI's executive officer and immediately infuse at least $1 million in cash that the news service says is critical to its survival. But even if the judge approves the agreement, he must also subsequently approve a plan of reorganization for the company, subject to a vote by UPI's creditors.

Beyond the issue of the sale, however, the judge also is expected to give an indication of whether the bidding process for the wire service should be reopened. Lawyers for FNN have argued that the bidding process that led to the agreement with Vazquez and Russo was unfair. This is the issue that attracted more than a dozen lawyers to the courtroom here over the weekend and that had yet to be decided as the hearing headed into the late hours Sunday night.

The three-day hearing dramatized the uncertainty that had once again crept into the deliberations over finding a buyer for UPI, which last April filed for protection under Chapter 11 of the federal bankruptcy code. The process was thought to have come to a close last month after UPI management, the union representing its workers and the committee of creditors endorsed the Vazquez-Russo offer. However, several potential complications have since arisen. Not only did FNN continue to press its bid, but the committee of creditors asked permission of the judge to consider that bid, which it says offers them more money.

At the hearing this weekend, however, Nicholson argued that the creditors committee was bound by its endorsement last month of the Vazquez proposal. UPI lawyers also argued that prompt approval of the sale agreement was required to ensure the survival of the wire service.

Jack Kenney, UPI's treasurer, testified that the company is projected to lose about $600,000 over the last quarter of 1985 and could not meet a cash shortfall by the end of the year without the immediate infusion of capital called for by the Vazquez agreement. UPI lawyer Richard Levine said such numbers illustrated the precarious nature of the wire service: "The longer there is the delay, the longer the customers and employes are going to be rolled back to the uncertainty that existed before."

FNN argued, however, that UPI's agreement to make Vazquez chief executive before a plan of reorganization is approved went beyond the scope of bankruptcy law. FNN lawyers also were expected to argue Sunday night that the bid process for the company was arbitrary, and that they had been unfairly denied a 48-hour extension they said FNN was promised by the creditors committee in order to revise its bid last month.

FNN attorneys were joined by lawyers for the creditors committee, who asked the judge to deny UPI's motion. They said that although quick action is needed to solve UPI's problems, there is still time to consider the FNN bid, and they asked the judge for a brief extension.