Once the odds-on favorite to win the award, Barkley's numbers slipped through the latter part of the season.
Love is second in the nation in rushing at 164.42 yards per game and is averaging 8.32 yards per carry.
Mayfield, a 6-foot-1, 220-pound senior, led Oklahoma to a No. 2 ranking and a berth in the College Football Playoff.
Jackson has the chance to become just the second two-time Heisman victor, joining Ohio State's Archie Griffin (1974 and 1975), but Mayfield, the 2016 runner-up, is the heavy favorite.
The junior was named on Monday night during ESPN'S Monday Night Countdown as one of the three finalists for college football's most prestigious honor, the Heisman Trophy Trust announced.
The Heisman Trophy will be awarded on Saturday night in NY.
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Jackson's 2017 season has been better than previous year with regards to his completion percentage and interception count, but his team's lack of success could be an issue for Heisman voters.
Jackson also leads the NCAA in total offense per game (411.0 total yards per game), total yards (4,932) and is tied for third in total touchdowns (42). Through the final five games, he failed to reach 100 yards rushing four times. 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.
He gained just 35 yards vs. Rutgers.
The Sooner quarterback finished with the second most passing yards in the country, piling up 4,340 through the air.
Barkley started the game at Ohio State with an incredible 97-yard kick return for a touchdown.