Krzyzewski, a 57-year-old Hall of Famer, has led the Blue Devils to three national championships in almost a quarter-century at the school.
Among Krzyzewski's former Duke players are Alaska high school stars Carlos Boozer of Juneau-Douglas and Trajan Langdon of East Anchorage, who both went on to play for the NBA's Cleveland Cavaliers.
"Coach K has informed us that the Los Angeles Lakers have contacted him and entered into serious discussions to fill their vacant head coaching position," Duke athletic director Joe Alleva said.
Lakers spokesman John Black said Kupchak met with Krzyzewski. "They talked about our coaching vacancy," he said.
Black said the team hasn't made a decision, and was considering several other candidates to replace Phil Jackson.
Alleva said he didn't know if the Krzyzewski and the Lakers were close to a deal.
"I haven't been privy to their conversations," he said. "But obviously, they are a great franchise."
Duke spokesman Jon Jackson said Krzyzewski was in Durham earlier Thursday. The Lakers declined to say where the discussions were held.
An attempt to reach Krzyzewski by phone was unsuccessful.
By Thursday night, about 100 students and fans gathered at "Krzyzewskiville" - the grassy plot outside Cameron Indoor Stadium where students camp out to attend Blue Devil basketball games - with signs and flags urging the coach to stay.
Duke president Richard Brodhead told The Associated Press he and Alleva had dinner with Krzyzewski on Tuesday, after Brodhead became aware that the coach had talked with the Lakers.
Brodhead said he didn't know if the Lakers offered Krzyzewski the job.
"If he has the offer, he's going to have a big decision before him," said Brodhead, who officially took office as Duke's president Thursday, succeeding Nan Keohane.
Brodhead said he and Alleva urged Krzyzewski to finish his career at the school.
"He means more to this place than the record of his victories, impressive though that is," Brodhead said. "He's a real teacher. He teaches character as well as basketball."
Krzyzewski has a 621-179 record in 24 seasons at Duke, leading the Blue Devils to NCAA championships in 1991, 1992 and 2001. Under Krzyzewski, the Blue Devils have 10 Final Four appearances, eight Atlantic Coast Conference tournament championships and 10 conference regular-season titles.
His Duke teams have been ranked No. 1 in 12 different seasons, including each of the last seven years.
"If he decides that he's had a great ride at Duke, but something else calls out to him now, we'd have to understand that," Brodhead said. "In the meantime, you can be sure we'll do all we can to persuade him that Duke and the college game are the right place for him."
The mother of incoming freshman David McClure, said her son was first informed of the news in a call from assistant coach Steve Wojciechowski on Thursday.
Betty McClure said she spoke with Krzyzewski over the weekend when the family brought the 6-foot-7 swingman to Durham for summer classes, and the coach gave no indication of leaving.
"They said that every year he gets approached by some team or another," she said from her home in Ridgefield, Conn. "And so, how can you really expend a lot of energy being angry or anything until you know what he's going to do?"