If a contract is finalized, Petrino will replace Charlie Strong.
Yahoo Sports has reported that Petrino's agent will meet with Louisville athletic director Tom Jurich on Wednesday night to finalize the contract and an announcement could be made as soon as Thursday morning.
Petrino, 52, got his start as a head coach at Louisville, leading the Cardinals from 2003 to 2006 before leaving for a brief stint as coach of the Atlanta Falcons.
Jurich targeted Petrino from the beginning and conducted brief phone conversations with several other assistants, including Derek Mason of Stanford and Pat Narduzzi of Michigan State.
Jurich believes Petrino can ignite the Louisville fan base with a return to explosive offensive football.
In addition, assistant Clint Hurtt, the Cardinals' top recruiter, is expected to be retained, according to a source. He is still serving a two-year show-cause penalty as a result of the NCAA investigation into the Miami Hurricanes-Nevin Shapiro scandal.
Petrino returned to the college ranks with Arkansas in 2008 but was fired in April 2012 for a "pattern of misleading behavior" following an accident in which the coach was injured while riding a motorcycle with his mistress, a former Razorbacks volleyball player.
In the wake of the scandal, Petrino signed a four-year contract with Western Kentucky in December 2012. The deal has a base salary of $850,000 and includes a $1.2 million repayment to the school if he terminates it early.
Petrino had a 41-9 record at Louisville, leading the Cardinals to a 12-1 mark and their first BCS bowl victory in the Orange Bowl in 2006.
He is 83-30 overall as a college coach, including an 8-4 mark this season with the Hilltoppers.
Strong, who guided the Cardinals to a 12-1 record this season, was introduced as Texas' coach Monday.
The Associated Press contributed to this report.