Appearing on JJ Redick's The Old Man and the Three podcast, Krzyzewski said he came "closer than any other offer I ever had" to leave Duke and become the Lakers head coach in 2004 (starts at 0:40 mark):
It was known at the time that Krzyzewski was in serious discussions with the Lakers. ESPN's Stephen A. Smith reported Coach K was offered a five-year, $40 million contract to replace Jackson, who didn't sign an extension after Los Angeles lost to the Detroit Pistons in the NBA Finals that year.
Krzyzewski told Redick that the Lakers also offered to finish paying for the Emily Krzyzewski Center, a nonprofit organization named after Mike's mother that operates in Durham, North Carolina.
"Your heart has to be in whatever you lead," Krzyzewski said in July 2004 of his decision to stay with Duke. "It became apparent that this decision was somewhat easier to make because you have to follow your heart and lead with it, and Duke has always taken up my whole heart."
The Lakers wound up hiring Rudy Tomjanovich, but he resigned 41 games into the 2004-05 season. Jackson returned to the team as head coach in June 2005, led them to three straight NBA Finals from 2008-10 and won consecutive titles in 2009 and 2010.
Since making his decision to stay at Duke, Krzyzewski has led the team to two more national championships in 2010 and 2015. He's also moved atop the all-time wins list in Division I men's basketball with 1,157 over 44 seasons between Army and Duke.