Kurdistan Democratic Party chief Masud Barzani said on Thursday that both Kurdish parties had agreed Jalal Talabani should be their candidate for one of the key posts in Baghdad.
"Either president or the prime minister, we will not accept other than that," Barzani said. Talabani is head of the Patriotic Union of Kurdistan, the other main Kurdish political party.
Together the two groups claim to represent about 90% of people in the Kurdish northern regions of Iraq. And despite fighting a civil war in the 1990s, both leaders formed an alliance to contest the elections.
The Kurdish alliance is widely expected to come second or third in the elections, with a Shia bloc certain to win.
Kurds represent about 15% of Iraq's 27 million strong population. They are mainly based in three northern provinces close to the Turkish and Iranian borders.
Turnout in Sunday's election is believed to have been very strong in the Kurdish region and the Kurds are expected to be powerful players when it comes to determining who takes the top positions in Iraq's next government.
Final results from the poll are not expected to be known for at least another week. Once the results are known, a 275-member National Assembly will be inaugurated and then a government formed.
The government will comprise a presidential council of a president and two vice-presidents, who will then decide on a prime minister and a cabinet of ministers.
Much of the horse-trading to determine the top four positions - president, vice-presidents and prime minister - is expected to take place in the days ahead, as the final results of the election are being determined.