According to SI.com's Chris Mannix, Colangelo said he felt it was time to move forward: "I love Carmelo. He made a great contribution. He was a very good international player. But for where we are and what we're doing, that conceivably could have been a distraction. I understand why the request was made. He's trying to reestablish himself. I think that has to be done in the [NBA]."
Anthony is an NBA free agent, as the 35-year-old has gone unsigned since the Chicago Bulls waived him in February. He last played for the Houston Rockets, who traded him in January.
Colangelo said one of Anthony's representatives reached out to let USA Basketball know that Melo had interest in playing for the team.
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Anthony is one of the most accomplished players in the history of USA Basketball. He has won four Olympic medals (three gold and one bronze), a World Championship bronze medal and a FIBA Americas Championship gold medal.
In addition to being the only man to win three Olympic golds for Team USA, he is the team's all-time leader in Olympic games played, points and rebounds.
After top stars such as Rockets guard James Harden, Los Angeles Lakers big Anthony Davis, Portland Trail Blazers guard Damian Lillard and Washington Wizards guard Bradley Beal pulled out of the World Cup in China, there was some thought that Anthony would be a good fit for Team USA.
Instead, Colangelo has elected to lean on a roster composed primarily of youngsters, such as Jayson Tatum, Donovan Mitchell, Kyle Kuzma, Jaylen Brown and Myles Turner, and a few veterans.
Melo's trainer, Chris Brickley, said last month on The Breakfast Club (h/t Dani Mohr of the New York Post) that Anthony wants an NBA farewell tour akin to the one Dwyane Wade had with the Miami Heat last season.
Playing for the U.S. and showing he has something left in the tank could have gone a long way toward convincing a team to take a chance on him.
The 17-year veteran is a 10-time All-Star and one of the most prolific scorers in NBA history, but he hasn't proved that he can thrive in a bench role, which is what he would almost certainly be relegated to at this juncture of his career.
As far as Team USA is concerned, look for veterans Kemba Walker, Kyle Lowry, Brook Lopez, PJ Tucker and Thaddeus Young to step into the leadership roles at the FIBA World Cup, which begins Aug. 31.