Good question.
A couple of years ago I predicted it would be somebody associated with the U.N., but nobody has really stepped forward yet.
I wouldn't get too starry-eyed yet. There's a long row to hoe before Iraq qualifies as stable, much less anything resembling a Western democracy. However, they have a good chance of being more of a democracy than any of their neighbors except Israel.
Western democracies are often based on the European "parliamentary" concept, and people sometimes forget that this was adapted from a specific culture and type of social organization. It worked to create a government from what used to be many smaller kingdoms or domains.
Maybe it's time to create something with a "House of Sheiks" in Iraq.