The article deals with the field of gifted children, who are considerably neglected from the point of view of programmatic and legislative approaches in the field of education in the Republic of Slovenia. The substantive research focus is therefore mainly on understanding and detailing the role of parents in discovering characteristics of potential giftedness and the role that parents have in promoting the child’s potential in one of the areas of giftedness. In the empirical part of the paper, we examined the extent to which parents perceive potential giftedness in their preschool children and whether they encourage them in developing their potential in different areas of giftedness. We used a descriptive, noncausal, and nonexperimental method. The survey sample included 201 parents of preschool children in the developmental period of early childhood from 4 to 6 years. Data were obtained using a questionnaire developed based on Giftedness Rating Scale to identify gifted children in elementary school and adapted to survey participants. Based on the established hypotheses, we reviewed the differences in the perception and promotion of different areas of potential giftedness in relation to the child’s gender and age, the parents’ educational level, and the outstanding strong area subjectively assessed by the parents. We also examined the relationship between the variables of perception and promotion of potential giftedness. The results of the study are relevant to the field of potentially gifted preschool children and the further recognition and promotion of their potential in kindergarten and in the family.