The two stars did not join the team on its flight to Atlanta on Monday, sources told ESPN.
The Clippers will be without their two best players and starting point guard Patrick Beverley (right knee soreness) as they carry a seven-game winning streak into Atlanta for the start of a six-game road trip.
Depending on the extent of the NBA protocols, Leonard or George could potentially join the team on this trip, sources said.
Leonard, George and Beverley played during Sunday's 108-100 win over the Oklahoma City Thunder. However, George was held out of the final four-plus minutes with hamstring tightness and Beverley did not play in the second half due to the knee injury.
Beverley also did not make the trip to Atlanta, sources said.
Leonard has been playing his best basketball of the season, averaging 32.3 points, 6.6 rebounds, 5 assists and 3 steals in the Clippers' past three wins.
George is enjoying a bounce-back season, averaging 23.9 points, 6.2 rebounds and 5.4 assists.