The Clippers didn't practice Thursday, giving the 6-foot-1 Collison some time to rest his injury before Los Angeles plays the Chicago Bulls on Friday night.
But after Wednesday night's game in Charlotte, N.C., and after Rivers talked about giving his point guard some time off, Collison seemed to be begging to stay on the court.
"I'll be better by Friday," Collison insisted. "It's one of those nagging injuries. I really don't want to sit."
The Clippers have a backup point guard in Darius Morris, but he's on a second 10-day contract that expires after Saturday night's game in Toronto.
That probably means Jamal Crawford, already the backup shooting guard and a backup point guard, will play even more minutes.
The shortage at point guard is difficult for the Clippers because Chris Paul remains sidelined because of a separation of his right shoulder.
"It's one thing when Chris is missing so everybody has to pick up their play for him," Crawford said. "If DC is missing, we're going to have to really clamp down and all of us have to step up."
Griffin, Paul make USA Basketball roster
Blake Griffin and Paul were selected to the USA Basketball 2014-16 roster Thursday.
Griffin and Paul are among 28 NBA players who were chosen to compete for 12 roster spots for the team going to the World Cup in Spain that starts in late August, and for the 2016 Olympic team in Brazil.
Griffin was one of the finalists for the 2012 Olympic team, but suffered a knee injury and wasn't able to compete.
But Griffin, who leads the Clippers in scoring (22.6 points) and is second in rebounds (10.0), is expected to compete for a spot on Team USA this summer.
Paul, who already has won two gold medals on Team USA, in 2008 and 2012, is not expected to play on the national team until the 2016 Olympics.