Two other nations, India and Thailand, are also interested in the job, which will be one of the toughest U.N. missions ever.
Diplomatic sources said U.N. Secretary-General Kofi Annan has already discussed the possibility with Pakistani President Pervez Musharraf.
The Pakistani ambassador in Washington, Ashraf Jehangir Qazi, is a career diplomat who has headed his country's missions in India and China as well.
The posting to India is considered the toughest diplomatic job in Pakistan because of the tense relations between South Asia's two nuclear states who have already fought three wars during the last 56 years.
As a senior Muslim diplomat, Qazi may be more acceptable to the Iraqis than others and his inclusion in the U.N. mission may also encourage Pakistan to contribute troops to a multinational force the United States is trying to raise for Iraq.
Martin Bashir resigns from MSNBC over Sarah Palin comments
Ron Burgundy interviews Peyton Manning on SportsCenter