UNITED NATIONS, OCT. 28 -- President Reagan is to receive an appeal from U.N. Secretary General Javier Perez de Cuellar on Thursday warning that the world organization will not be able to cover its expenses in December and could be driven to bankruptcy unless the United States pays part of this year's dues within weeks.

The letter, urging White House efforts on Capitol Hill, where an appropriations bill containing partial U.S. contributions is in conference committee, will be delivered by American Ambassador Vernon Walters, U.S. and U.N. officials said today. Walters is expected to bolster the plea by arguing that U.S. interests will be severely damaged by a failure to sustain the organization at a time when U.S. policy in the Persian Gulf depends on action by the U.N. Security Council.

"That is just one of the issues that the United States needs the U.N. for," said one American official. "If the Russians win here by paying their bills when our default continues, we'll be pulling the rug out from under ourselves, and have only ourselves to blame."

The letter from Perez de Cuellar outlines the United Nations' financial plight and says that "unless the United States comes through, this organization is driven to bankruptcy." It ends: "With your help, perhaps the situation can be saved."

U.N. and U.S. officials said that the groundwork for the plea had already been prepared in the White House, and that there were indications of sympathy from the office of chief of staff Howard H. Baker Jr., despite Washington's preoccupation with cutting the budget.

The appropriation for the United Nations is part of the fiscal 1988 budget now before Congress. The Senate version would provide $141.7 million and the House version $97.5 million, before anticipated deductions mandated by the Gramm-Rudman-Hollings deficit reduction act.

The world body has become increasingly unpopular on Capitol Hill even as Reagan administration support for it has grown. U.N. officials said they recognized the difficulty of their request for a special exemption from budget strictures, but they expressed confidence that Washington would not let the United Nations become bankrupt.

The United States owes $414 million in U.N. dues, including all $212 million for the 1987 regular budget. By comparison, the Soviet Union -- which until recently had long had outstanding debts -- has paid this year in full and announced that it will repay arrears dating back to the 1950s.

A year ago, Moscow, Washington and other major contributors negotiated an agreement with the United Nations' Third World majority by which decisions on a budget ceiling and spending priorities would be made by consensus, rather than majority vote. This would give the few big donors greater influence. But in return, the United States and others were to pay what they owed.

The U.S. failure to pay threatens that agreement, which remains to be tested in the General Assembly in December. The funding crisis also has raised the issue of whether Washington should continue to pay 25 percent of the U.N. budget. Several delegations have proposed that U.S. payments be cut back to 10 or 15 percent. Washington opposes this because it would reduce the number of U.N. jobs held by Americans and curtail U.S. influence.

U.N. officials said Washington remains the only source of funds for December and that without it, 10,000 to 12,000 U.N. workers around the world might not be paid for the month. U.N. officials conceded that a U.S. rejection would prompt pleas for donations from other countries, but they said they could not be sure of getting any.