Jackson, who is looking to join Ohio State's Archie Griffin (1974, 1975) in accomplishing the feat, joined Oklahoma quarterback Baker Mayfield and Stanford running back Bryce Love in being named as Heisman finalists on Monday.
The winner of the award, which goes to college football's most outstanding player, will be revealed Saturday night at the Downtown Athletic Club in New York.
Jackson completed 60.4 percent of his passes for 3,489 yards with 25 touchdowns and six interceptions for the Cardinals (8-4). The dual-threat quarterback also rushed for 1,443 yards and 17 rushing scores to help Louisville earn a spot in the TaxSlayer Bowl.
Mayfield has thrown for 4,340 yards with 41 touchdowns and five interceptions this season for the second-ranked Sooners, who will play No. 3 Georgia in a College Football Playoff semifinal at the Rose Bowl on New Year's Day. The senior, who finished third in the Heisman voting last season, boasts a 71.0 completion percentage and has rushed for 310 yards and five touchdowns.
Love is attempting to become the first Stanford player to win the Heisman since quarterback Jim Plunkett in 1970. Love, who played in the shadow of 2017 first-round pick Christian McCaffrey, has rushed for 1,973 yards and 17 touchdowns in 12 games for the Pac-12 North champion Cardinal this season.