According to Wikipedia:
Larry Mikan, 28, 1969-70 season against Michigan
2nd place: Ron Johnson, 27, 1957-58 season against North Carolina
Those were in the older era, though. Before the mid-seventies, national rebounding leaders routinely averaged over 20 rebounds per game. Oscar Tshiebwe of Kentucky averaged 15.2 this season and that was the highest average since 1979. A guy who entered the portal a couple of weeks ago from Utah Valley averaged 15 per game last year (the second highest average since 1980) but that was in a shortened 22 game season.