The Times-Picayune was first to report the potential extension, which is still in the process of being finalized.
LSU’s board of supervisors, which would have to approve the contract, does not meet again until March 15.
Orgeron, 57, was named the team’s interim coach in 2016 upon Les Miles’ firing and was installed on a permanent basis the following offseason. A Louisiana native, he has posted a 25-9 record overall in Baton Rouge.
The Tigers, who were picked to finish fifth in the SEC West in 2018, instead placed second behind conference champion Alabama. The team won the PlayStation Fiesta Bowl, beating UCF 40-32.
Orgeron’s current contract, which runs through 2021, pays him $3.5 million per year.
LSU, which returns starting quarterback Joe Burrow, opens next season at home Aug. 31 against Georgia Southern before going on the road to Texas the following weekend.