The U.N. chief urged the council to try again to conduct a referendum, revise an autonomy proposal, or consider dividing the territory.
In a report to the council, Annan said the United Nations faced "a rather bleak situation" because neither the Moroccan government nor the Polisario Front rebels which fought a 15-year war over the territory have been willing to negotiate a solution.
After Spain abandoned the mineral-rich desert region on the Atlantic coast of north Africa in 1975, Morocco annexed it and moved settlers in. Some 200,000 local Saharawi people fled into exile and still live in refugee camps in southeast Algeria.
Fighting ended in 1991 with a U.N.-negotiated cease-fire that called for a referendum on whether Western Sahara would become independent or part of Morocco. But U.N. efforts to identify voters have been frustrated by disputes over who is eligible which has led to 131,038 appeals over the U.N. list of potential voters.
Former U.S. Secretary of State James A. Baker III has spent the last five year trying to negotiate an end to the protracted conflict.
Annan said he and Baker believe there are four options for the council:
Resume efforts to try to hold a referendum by starting the very lengthy appeals process.
Baker could revise the autonomy plan taking into account the concerns expressed by the parties.
The council could ask Baker to explore a possible division of the Western Sahara.
The council could terminate the U.N. mission, "thereby recognizing that after more than 11 years the United Nations is not going to solve the problem.
To give the council time to decide, he asked for the U.N. mission, which currently has 203 military observers and 25 civilian police, to be extended for two months until April 30. It currently expires Feb. 28.