Kardashian had expressed a desire for Odom to represent the US in the 2012 Games, with Odom expected to take part in this week's training camp.
USA Basketball chairman Jerry Colangelo has now confirmed that Odom has backed out of the Olympics training camp, according to The AP.
Odom had been considered a long-shot to make the US team, but could have made the cut due to injuries of other high-profile NBA stars.
Kobe Bryant, LeBron James, Carmelo Anthony, Chris Paul and Kevin Durant are among the professional basketball stars all expected to compete at this week's Team USA training camp in Las Vegas.
NBA star Tony Parker's own hopes of competing in the London Games on Team France were thrown into doubt last month when he suffered a scratched cornea in Drake and Chris Brown's club brawl.