The identity of the individual who tested positive is not known.
The decision to close the facility was reportedly precautionary. The team could still reopen the gym before it travels to Florida on July 8, sources told Wojnarowski.
To date, there have been no other reported positive test results within the organization. Clippers head coach Doc Rivers said this week he was unaware of any players or staff testing positive.
"Not that I know of," he said Wednesday, according to the Orange County Register's Mirjam Swanson. "Again, I wouldn't even know that information, which is good. I think so far, at least in our homestead, so far, so good.
"Guys have done a great job trying to protect themselves, but this virus, he's a mean customer. So we're just doing our best here."
The NBA announced earlier Thursday that nine of 344 players tested between June 24-29 had their results come back positive, as did 10 of 884 staff members.
The Denver Nuggets also reportedly shut down their training center Tuesday following positive coronavirus tests within their party.