The person spoke to The Associated Press on condition of anonymity Tuesday because Cornell had not yet announced the hire.
The Ivy League university has scheduled a news conference for Wednesday regarding a replacement for Jim Knowles, who resigned in December to become defensive coordinator at Duke.
Knowles was 26-34 in six seasons and Cornell was 2-8 in 2009, the school's worst record since 2003.
Austin is a former Rebels quarterback. He was the offensive coordinator at his alma mater for two seasons. Austin helped guide the Rebels to back-to-back, nine-win seasons for the first time in nearly 50 years.