Rodriguez, the former coach at West Virginia, Michigan and Arizona, completed his first season at ULM under coach Terry Bowden. Earlier this month, Jacksonville State coach John Grass announced he was stepping down after going 72-26 in eight seasons with the FCS program.
Jacksonville State also earlier this month accepted an invitation to join Conference USA and compete in the FBS beginning in 2023.
Rodriguez, 58, last served as a head coach at Arizona, going 43-35 in six seasons before being fired in January 2018. Arizona investigated allegations from a former administrative assistant throughout the fall of 2017 and could not substantiate them, but it became aware of information that caused concern for administrators and ultimately led to the dismissal.
A lawsuit alleging sexual harassment and a hostile workplace environment against Rodriguez and Arizona was dismissed earlier this month, with both sides only paying their own costs and attorneys' fees.
Rodriguez is 118-83 as an FBS coach.