A source with knowledge of the situation, speaking on condition of anonymity, said a formal announcement will be made on the eve of the start of Team USA's minicamp later this month.
The story was first reported by the Boston Globe.
USA basketball managing director Jerry Colangelo has been lobbying Coach K for months to stay in the job he held when the Americans won the gold medal in Beijing last summer.
"With the success that we had, I would do everything in my power to keep everything intact," Colangelo told The Associated Press without confirming the decision.
"I'm a strong believer in not upsetting the apple cart."
Krzyzewski led the Americans to a 36-1 record from 2006-08, and a return would give him a chance to fill one of the only holes on his Hall of Fame resume. He is 0-for-2 in the world championships, also finishing third in 1990 with a team of college players.