Problem construction and divergent thinking (DT) are considered to be indicators of creative potential. Previous studies, with different goals, suggest a positive correlation between problem construction and DT. However, none of these works have explicitly examined which index of DT is more associated with problem construction. The current investigation examined the association between problem construction and three main indexes of DT: fluency, flexibility, and originality. It also tested whether such a relation differs based on task nature (verbal versus figural). The sample consisted of 90 sixth graders who completed three tests: (a) a verbal DT test, (b) a figural DT test, and (c) a problem construction test. Correlational analysis showed that flexibility was highly correlated with problem construction in the verbal DT test, whereas originality was highly correlated with problem construction in the figural test. The association between problem construction and verbal versus figural DT significantly differed in all DT indexes. This finding suggests that figural and verbal tasks assess DT in a different way, which was confirmed by a canonical correlation analysis. Finally, results of a multiple regression analysis showed that verbal DT significantly explained 59% of the variance in fluency scores in problem construction and 60% in originality scores in problem construction. Meanwhile, figural DT explained 8% to 9% of the variability in fluency and originality scores in problem construction. As suggested by experts in the field of problem construction, the role of flexibility in problem construction is a fertile area to be considered in future studies.