The White House is reviewing various options, but says troops would only stay if Iraqi officials make a specific request.
Wendy Sherman told her Senate confirmation hearing Wednesday that the issue centers on Iraqi government interest in U.S. military trainers remaining in the country.
Sherman is the nominee to become the undersecretary of state for policy.
Currently, there are about 46,000 U.S. troops in Iraq. The White House has offered to keep as many as 10,000 there.
A 2008 security agreement requires all U.S. troops to be out by Dec. 31, but the deadline is being reconsidered due to Iraq's shaky security situation.
Pentagon press secretary George Little said the State Department is leading the troop discussions with Iraq. He declined to discuss the internal deliberations.
The Associated Press contributed to this report.