Griffin, who signed a five-year contract extension with the Clippers worth nearly $100 million this week, is expected to be sidelined for eight weeks, the Times reported, citing NBA executives as sources.
Griffin complained of soreness in his knee the day after a full scrimmage with the champion US Olympic team in Las Vegas and returned to Los Angeles for a medical examination, with his NBA coach also suggesting he had been ruled out of the Games.
"Missing out on the Olympic experience will be tough for him to take. I know how dedicated he was to doing that," Clippers coach Vinny Del Negro said.
"We're glad we can get this fixed now and take advantage of the available time for him to fully recover (and) we're relieved that this does not affect Blake's ability to be ready in time for (NBA) training camp."
The Clippers said Griffin would be further evaluated by a specialist on Sunday, while the newspaper said it was likely he would undergo arthroscopic surgery next week.
The forward, who averaged 20.7 points and 10.9 rebounds last season and is known for his electrifying dunks, missed Thursday's 113-59 US romp over the Dominican Republic in the team's first of five games in their run-up to the Olympics and was replaced by Anthony Davis.
Davis, the number one pick of the NBA Draft by the New Orleans Hornets after being named college player of the year after leading Kentucky to the NCAA championship, scored nine points after entering the rout in the fourth quarter.
Earlier, USA Basketball chief Jerry Colangelo said Griffin would have to formally withdraw from the team before Davis, an alternate on the roster, could officially take his place.
"As we understand it, he hurt his knee at the end of the (NBA) season and had a decision to make about being scoped (arthroscopic surgery) or not," Colangelo said during ESPN's broadcast of the game against the Dominican Republic.
"He decided not to. He seemed really strong at camp and had no issues. Even yesterday he had a terrific workout. He felt great last night but woke up with some discomfort and some swelling so now we wait to see what's going to take place."
Colangelo said Davis would stay with the team until a determination was made about Griffin's status.
Griffin is just the latest in a long string of US players hit by injuries ahead of the London Games.
The Americans have four more games before the Olympics.
They will train in Washington, DC, from July 13-15 and play Brazil at the Verizon Center on July 16 before moving to Manchester to play Britain on July 19 and then go to Barcelona for games against Argentina on July 22 and Spain on July 24.