The Clippers have back-to-back road games against the Houston Rockets on Wednesday and the Pelicans on Thursday. George is listed as questionable for Wednesday's game.
George went through his first full live contact practice of the season Saturday, and coach Doc Rivers said the Clippers pushed him in the practice to ramp up his conditioning.
George, 29, underwent rotator cuff surgery to repair a partially torn tendon in his right shoulder in May and minor surgery to repair a partial tear of his left labrum in June. The Clippers traded for the perennial All-Star in July with the expectation he'd miss training camp and potentially the start of the season as he recovered from his injuries.
He averaged a career-best 28 points for the Oklahoma City Thunder last season and was a finalist for both NBA MVP and Defensive Player of the Year. He led the league with 2.21 steals per contest.
Meanwhile, an MRI performed on Clippers guard Landry Shamet's left ankle showed he suffered a grade 2 high ankle sprain, league sources told ESPN. A timeline for his return is to be determined.
Shamet is listed as out for Wednesday's game against the Rockets. Kawhi Leonard, who did not play in the first game of the back-to-back sets in each of the previous two weeks, is not on the injury report for that game.