Craig, the top lawyer at the White House and a close aide to President Barack Obama, has helped lead the administration's efforts on several national-security issues that once enjoyed popularity but have since become become political liabilities for Obama.
These include the closure of the prison at Guantanamo Bay, Cuba, the release of Bush administration-era national-security documents, and efforts to find legal ways to indefinitely hold some detainees who can't be put on trial.
The decision to close the Guantanamo facility became a political problem for Obama when concerns arose that some of the detainees would be released into the U.S. and the public soured on the move.
Craig didn't respond to questions about his job as White House counsel for this article.
The people familiar with the matter said a final decision hasn't been made.