That has forced the Americans to change their plans of announcing their 12-man roster in late May. Colangelo, meeting with Krzyzewski and his staff Monday and Tuesday in Las Vegas, said the roster likely will now be chosen much closer to the June 18 deadline.
The Americans had named a pool of 20 finalists in January, but with candidates Chauncey Billups and LaMarcus Aldridge already lost to injuries, they may now be forced to add players just so they have the allowable six alternates.
"On the injury side, no news is good news, and that's not the way it's been," Colangelo said. "You take two out of your potential 12 and they go down and they're out, that's a blow no matter what. The important thing now is to focus on who would be, what would the makeup be of a roster."
Former Brazil players Hortencia and Paula, silver medalists at the Atlanta Games in 1996, participated in the women's draw in Rio, which will host the 2016 Games. Oscar Schmidt, Brazil's career scoring leader, helped in the men's draw.
"The 2008 men's final between the U.S. and Spain was one of the greatest Olympic moments," said FIBA Secretary General Patrick Baumann, an IOC member. "It showed the huge strides international basketball had made in becoming more and more competitive. I expect this year's Olympic basketball tournaments will be a great and memorable spectacle for all."
Both sides will be short-handed if there's a rematch, the Spaniards having already lost point guard Ricky Rubio to a knee injury during what had been a stellar rookie season with the Minnesota Timberwolves.
The Brazilian men's team will be playing in the Olympics for the first time since the Atlanta Games. It had failed to qualify for the last three Olympic tournaments.
Other teams participating in the men's Olympic qualifying tournament will be Angola, Dominican Republic, Macedonia, Jordan, South Korea, New Zealand, Nigeria, Puerto Rico, and host Venezuela.
The women's tournament will include Argentina, Canada, Croatia, Czech Republic, France, Japan, South Korea, Mali, Mozambique, New Zealand, Puerto Rico and host Turkey.
AP Basketball Writer Doug Feinberg contributed to this report.
Follow Brian Mahoney on Twitter: http://www.twitter.com/Briancmahoney
Copyright 2012 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.