"There are several possibilities of how things can be managed," department spokesman Richard Boucher said.
His comments followed remarks by U.S. Administrator Paul Bremer who told the Washington Post: "If they ask for him (Saddam Hussein), which I have every reason to believe they will ... we'll turn him over. Legal custody and physical custody can be two separate things."
Iraqi Prime Minister Ayad Allawi has said Saddam and others should be transferred to Iraqi control by the June 30 hand over of sovereignty.
However, President George Bush has said Saddam and others would be turned over only when "appropriate security" is in place.
The United States has held Saddam at a secret location since his capture last December.