The rankings represent Kiper's final big board before the official start of the 2018 college football season.
Oliver, who is set to enter his junior season, is coming off two highly productive campaigns at Houston.
Last season, Oliver registered 73 tackles, including 16.5 for loss, as well as 5.5 sacks and two forced fumbles. As a freshman, Oliver finished with 65 tackles, 22.0 tackles for loss, 5.0 sacks and two forced fumbles.
Kiper wrote that while Oliver is "not quite [Los Angeles Rams defensive tackle] Aaron Donald," he will likely continue to draw comparisons to him.
Oliver has good size at 6'3" and 292 pounds, and he is also an elite athlete with a quick first step who is equally effective as a pass-rusher and a run-stuffer.
According to OddsShark, Oliver is tied with Ohio State defensive end Nick Bosa for the best odds among defensive players to win the Heisman Trophy this season at 125-1 (+12,500).
The last primarily defensive player to win the Heisman Trophy was Michigan cornerback Charles Woodson in 1997.
If Oliver goes No. 1 overall in the 2019 NFL draft, he will be the second defensive lineman to be selected with the top pick in three years, joining Cleveland Browns defensive end Myles Garrett, who went No. 1 in 2017.
No defensive tackle has gone No. 1 overall since the Cincinnati Bengals took Dan Wilkinson in 1994.
Oliver will open his 2018 regular season Saturday against the Rice Owls.