Hill has extensive experience in Europe. If formally nominated by President Barack Obama and confirmed by the Senate, he would replace Ryan Crocker, an Arabic speaker who has served as US ambassador to Syria, Kuwait and Lebanon.
"For the secretary and, of course, for the president, Iraq is a high priority and they are looking at Iraq policy and when we have a nomination to put forward, the White House will make that public," said State Department spokesman Gordon Duguid.
News that Hill was in line for the job was first reported by ABC News on its website.
Obama spoke with Iraqi Prime Minister Nuri Al Maliki and President Jalal Talabani to congratulate them on the provincial elections held on Saturday, White House spokesman Robert Gibbs said in a statement.
"The president offered the best wishes of the American people as Iraq's new provincial leaders begin to assume important new responsibilities on behalf of the Iraqi people."
Obama also discussed plans to reduce the US military troops’ presence in Iraq.
The United States invaded Iraq in March 2003 to topple former dictator Saddam Hussein, igniting a brutal sectarian war that has slowly subsided.
Obama pledged in his presidential campaign to withdraw all US combat troops from Iraq within 16 months and on Sunday said that a substantial number of the 140,000 US soldiers would leave within a year.
Iraqis on Saturday held their most peaceful election since the fall of Saddam, voting for provincial councils without a single major attack in a poll that demonstrated the country's dramatic security gains.
However, analysts say Iraq remains fragile despite the gradual reduction of violence that followed former US President George W Bush's "surge" of US troops in 2007.
Hill has spent the past four years as assistant secretary of state for East Asian and Pacific affairs and as the senior US official in multilateral talks on ending North Korea's nuclear programmes.
Earlier in his career, he served as ambassador to South Korea, Poland and Macedonia and as special envoy to Kosovo. He speaks Polish, Serbo-Croatian, and Macedonian.