Spurs general manager RC Buford said in a statement they "always support a player's decision when it comes to participation with his national team."
Aldridge joins Golden State Warriors guard Stephen Curry, who announced his removal from consideration Monday, and four other top players from USA Basketball's original 31-man player pool to skip the Olympics due to health.
Team USA chairman Jerry Colangelo told ESPN on Monday that, to this point, no players in USAB's Olympic player pool have withdrawn from consideration for this summer's Rio Games due to Brazil-related concerns.
Amid rising angst from some Olympic-bound athletes about the conditions in Brazil and fears of outbreaks of the Zika virus, Colangelo said the only players to date no longer available for selection are the aforementioned six players dealing with current or recent injury issues.
Curry became the latest prominent member of that group Monday, when he announced that -- despite his well-chronicled desire to make his Olympic debut this summer -- he felt the need to take the summer off from national team duty in the wake of his knee and ankle injuries suffered in this year's playoffs.
"We've had no others [withdraw from consideration]," Colangelo said by phone Monday. "Everyone else seems to be right in line.
"[LeBron] James was the only guy we knew wouldn't make a decision until his season was over, which means after the Finals. So we've been looking at roster makeup with or without LeBron. There will be tweaking without him if he decides he's unable to play. With him, we feel we are pretty close to what we're going to go with. Without him, we'll tweak it."
USA Basketball has been planning for months to announce the official 12-man roster for Rio in late June, after the Finals and NBA draft but well before the group convenes in Las Vegas in mid-July for its first training camp.
Curry's Warriors teammates Draymond Green and Harrison Barnes likewise both told Spears on Monday that they remain available and hopeful of being selected to the final 12-man roster, while a source close to the situation told ESPN that Warriors guard Klay Thompson also remains intent on playing for Team USA in the Olympics.
Spain center Pau Gasol of the Bulls said late last month that he is considering skipping the Rio Olympics due to concerns over the Zika virus, becoming the most prominent NBA player to speak out about the issue thus far.
"It wouldn't surprise me to see some athletes deciding not to participate in the Games to avoid putting their health and the health of their families at risk," Gasol said. "I'm thinking about [whether to go]. Just like every athlete or any other person considering going to Rio should be thinking about it."
Reached Monday by ESPN, Australia center Andrew Bogut of the Warriors said: "I am 100 percent committed [to playing this summer] as of now, but am following the events in Brazil closely and would be lying if I said they are not becoming somewhat concerning as we get closer to the event."
The Olympic Games in Rio de Janeiro run from Aug. 5-21.
Information from The Associated Press was used in this report.