CHICAGO—Amid an intense national furor over the fairness of college admissions, the Education Department is looking into a tactic that has been used in some suburbs here, in which wealthy parents transfer legal guardianship of their college-bound children to relatives or friends so the teens can claim financial aid, say people familiar with the matter.

The strategy caught the department’s attention amid a spate of guardianship transfers here. It means that only the children’s earnings were considered in their financial-aid...