Iraqi legislators have sought to divide equally power in the regional council among Kirkuk's three main groups - Arabs, Kurds and Turkmen. But Kurds, who constitute a majority, are vigorously opposed to the plan.
Kurds generally have favoured using a 2009 voter registry, which probably reflects the Kurdish population growth.
Arabs prefer a 2004 voter registry, when the Kurdish population was not as large in Kirkuk.
Alaa Maki, an Iraqi member of parliament, told Al Jazeera that progress in parliament is very slow on the matter.
"The Arabs and the Turkmen have agreed on a proposal ... now we are waiting for the Kurdish side to study the proposal and give their view," he said.
"If we reach an agreement, even if it is tomorrow, Friday, we might have a meeting to pass the law.
"The demographics have changed in the north. The Arabs and the Turks want fair representation [of this]. They don't want to pass the electoral law in the current situation as it would then be the basis for all future situations demographically."
Any delay in the elections could plunge Iraq into a worsening crisis, undermining the government and leading to instability just as US troops are preparing to withdraw, a process that was scheduled to gather pace after the vote.
Ghassan al-Atiyyah, an Iraqi politician, says that while parliament has the authority to extend the election date for two weeks, it is doubtful whether it would lead to new alignments or coalitions in the country.
"US military officials say that if there is a delay, the American schedule to leave Iraq will have to be reconsidered," he told Al Jazeera on Thursday.
"That would put Iraq in an even worse situation than it is in now. The real stumbling block is Kirkuk. Each party feels a compromise is needed."