The State Department will allow Nicaraguan President Daniel Ortega to visit the United Nations on Monday even though his visa application was filed too late for the normal processing period, it was announced Friday.

Privately, U.S. officials said Ortega plans to meet with Soviet President Mikhail S. Gorbachev, who will address the U.N. General Assembly next week and will meet with President Reagan and President-elect George Bush.But sources close to the Nicaraguan government, insisting on anonymity, said Ortega's main purpose in visiting the United Nations will be to discuss the effects on Nicaragua of Hurricane Joan, which devastated broad areas of the country in October.

The sources said Ortega wants to appeal for additional international assistance before the effects of the disaster become a forgotten issue. They were unaware of any plan by Ortega to meet with Gorbachev.

State Department deputy spokeswoman Phyllis Oakley said visas were approved for Ortega, his wife, Rosario, and his son, Rafael, for travel on Dec. 5. They will be accompanied by Ortega's physician and 14 security guards.

Oakley said their applications were expedited even though they were not received within the 15 working days the U.S. Embassy in Managua requires for processing.