The Longhorns (2-2) will face rival Oklahoma next Saturday in Dallas. Last year, Texas limped into the OU game with a 1-4 record but pulled off the upset.
This year's Oklahoma game is critical for Strong, but his future does not depend on the outcome, the source said. If the Longhorns continue to struggle, though, the most likely scenario is that the defensive staff would be sacrificed for Strong to return in 2017, the source said.
After Saturday's 49-31 loss at Oklahoma State, Texas athletic director Mike Perrin told ESPN's Jake Trotter that "I'm not evaluating Charlie, per se. I'm evaluating everything."
Longhorns spokesman John Bianco later said Perrin's comments were about the coaching staff needing to evaluate the game and the issues the team had on the field.
After starting the season 2-0, the Longhorns have lost two straight -- to Cal and Oklahoma State -- giving up 99 total points in the two defeats.The loss marked the third time in four games this year that Texas has allowed at least 47 points in a game.
"You can't play the way we played in the first half and expect to win a football game, especially in a tough environment like this," said Strong, whose Longhorns trailed 37-25 at the half.
Strong is in the third year of a five-year deal. If fired after the season, he would receive a $10 million buyout.
The Associated Press contributed to this report.
Texas sticking with Strong for at least rest of season
Brett McMurphy has the latest regarding Charlie Strong's future at Texas and says if struggles continue, expect the defensive staff to be sacrificed.