Diplomats said the request would be presented on Monday by US occupation administrator in Iraq, Paul Bremer, to UN Secretary-General Kofi Annan.
Bremer, Annan and a delegation from the US-appointed Iraqi Governing Council are due to discuss Iraq's political future in a high-stakes meeting in New York.
The meeting has taken on new urgency since the spiritual leader of Iraq's Shia Muslims, Grand Ayat Allah Ali al-Sistani, demanded direct elections before the planned handover of power to Iraqis on 30 June.
Sistani has rejected the caucus system planned by the Governing Council and the US-led coalition, which would lead to the creation of a caretaker government but would not allow for elections until next year.
On Friday, Sistani threatened mass protests, including a general strike, if the US-led coalition does not agree to the direct vote.
The 73-year-old cleric, long known as a "moderate" who steered clear of politics in the early months of the occupation and drew praise from the United States, could now derail the handover plans.
"There is generally a perception that early elections tend to favour the extremes rather than the moderates, and they also have a risk in a polarised society like Iraq of cementing that polarisation... People are worried that they are going to be cheated out of the real fruits of democracy, and the UN has no interest in contributing to that"
Annan has already indicated he agrees with the United States that there is not enough time to organise credible elections before the end of June.
The diplomats said a fact-finding team could either convince Sistani the elections are not feasible, or find a compromise that would avoid a showdown between the US-led coalition and the widely respected cleric.
The stakes are high for the United States and for Annan, who pulled UN staff out of Baghdad after a series of deadly attacks on aid agencies, including a truck bombing that killed his top envoy in Iraq and 21 others in August.
Annan has indicated he is unwilling to send his personnel back into Iraq unless he is satisfied the security situation is improved, and the world body will be given a substantive role to play.
UN and US officials declined to comment on a potential UN mission, but a senior UN official said early elections were a tremendous risk as the nation tries to shift towards democracy.
"There is generally a perception that early elections tend to favour the extremes rather than the moderates, and they also have a risk in a polarised society like Iraq of cementing that polarisation," the official said.
"People are worried that they are going to be cheated out of the real fruits of democracy, and the UN has no interest in contributing to that."
Although no reliable census exists in Iraq, the Shia Muslims led by Sistani - who were brutally repressed under Saddam Hussein - are believed to be a sizeable majority.
Sistani has said he wants the United Nations to return to Iraq for a first-hand look at whether the elections could be quickly put together.
Bremer wants a US-appointed
government to rule Iraq till 2005
"We'll have to see if that's one of the things they ask" on Monday, the UN official said.
Adnan Pachachi, who will lead the Governing Council delegation at Monday's meeting, has said that insisting on elections could mean delaying the handover of power for two years, leaving Iraqis "extremely disappointed and frustrated."
However, he suggested there could be changes to the current plan.
In Washington, where Bremer was meeting with US officials to prepare for Monday, a White House spokesman said there were talks on how to "refine or improve" the handover.