Ban Ki-moon said simmering tensions between the independence-minded ethnic Albanians and Serbs, who want to keep the province within Serbia, could boil over if no deal was reached soon, according to an advance copy of the report made available to The Associated Press.
"There remains a discernible underlying volatility in Kosovo, which has been accentuated by disappointment expressed by the people of Kosovo at the prolongation of the Kosovo future status process," Ban said. The report is to be submitted to the U.N. Security Council next week.
The process must reach a conclusion, he said, or else parties will face the risk of "progress beginning to unravel and of instability in Kosovo and the region."
International envoys said on Friday that both sides, which met in New York, appeared determined to bring the peace process to a successful end.
It was the first meeting between the rival sides since Serbia earlier this year rejected a U.N. plan to grant Kosovo supervised independence. Another round of face-to-face discussions is scheduled for Oct. 14 in Brussels.
Ban said in the report that unresolved differences between Serbia and ethnic Albanians could again lead to failure in the talks.
"Consideration should be given as to how to deal with a situation in which the sides are unable to reach an agreement by the end of the current period of engagement," he said.
International envoys are to report to Ban on the progress of the talks by Dec. 10.
The U.S. supports Kosovo becoming an independent state, but Russia opposes the drive, with some EU countries worrying over whether to recognize an independent Kosovo if talks fail.
Some 10,000 people died during the 1998-99 war, and some 2,000 remain missing in the aftermath of a brutal crackdown by Serb forces on separatist Albanians.
The onslaught prompted NATO to wage an 78-day air war against the former Yugoslavia to try to end the fighting.