Krzyzewski, who joined Calipari for a 30-plus-minute conversation taped Thursday but released to ESPN in advance of Tuesday's posting on iTunes, Stitcher, SoundCloud and Google Play, said the much-maligned Cousins was one of many former Calipari players whom he enjoyed coaching with Team USA.
The three-time gold-medal-winning coach praised Cousins for sticking with Team USA after initially being on the USA Select Team in 2012 following his one season at Kentucky in 2009-10. Cousins was added to the national team in 2014 and won gold medals at that year's world championship in Madrid and the Rio de Janeiro Olympics this past summer.
"For him to come back and still want it, it said a lot about how much he wanted to do it," Krzyzewski told Calipari. "He came through for us big time. He's tough as hell. He is so damn talented. I don't think he has a position. You can't call him a 5 or a 4. Just call him a great player."
Cousins has said he wants to play for Team USA in 2020, when San Antonio Spurs coach Gregg Popovich will replace Krzyzewski.
Krzyzewski told Calipari that the toughest player he has coached against was Argentina's Manu Ginobili of the Spurs. He added that Spain's Pau Gasol, now also on the Spurs, was a tough competitor for him during international competition.
On his longevity at Duke over the past 37 years, Krzyzewski told Calipari that he doesn't think he could be in a rebuilding position. He said he has been able to work with talented players who are able to play at the highest level of competition.
"When you recruit good people and are doing what you love, you stay pretty young," said Krzyzewski. "I'm 69 now, and I feel a lot younger. I've been fortunate to lead a good life at West Point and at Duke."
Krzyzewski said he made a conscious decision 25 years ago to hire former players on his staff only as long as there were enough of them who wanted to be a coach and could coach.
The two discussed their childhoods being raised by immigrant parents, their shared Catholic faith and their basketball inspirations. Calipari also admitted that Kentucky fans probably wouldn't want to hear that he is a big fan of former Duke star Christian Laettner.
Calipari told Krzyzewski that he hoped Kentucky and Duke get to play each other at the Final Four in April in Glendale, Arizona.
"In 2015, we screwed that up," Calipari added, referring to Kentucky losing to Wisconsin in the national semifinal before Duke beat the Badgers in Arlington, Texas.
Krzyzewski told Calipari it would be an honor to play Kentucky in the Final Four.
Calipari also praised Krzyzewski, saying, "What you've done for the game is incredible. What you've done for your school is incredible, for the country, for coaches. I love what you've done for your players and your staff."
The one topic the two didn't discuss was recruiting and the NBA's one-and-done era, something both Hall of Fame coaches have flourished in.