Studies related to creativity generally investigate brain activity at rest using raw scores from only one creative task. However, considering all the factors that can impact the creative product, we believe that the creative potential of individuals must be evaluated to identify the associated resting-state brain networks. Moreover, studying the brain functional connectivity related to creativity processes should be considered in conjunction with cognitive functioning as both are composite phenomena. To test this assumption, in this exploratory study, we differentiated high- and low-creativity potential people with a cognitive functioning approach using structural equation modeling assuming an influence of working memory (WM) and analytical thinking on creativity assessed by the Torrance Tests of Creative Thinking. Then, we examined brain functional connectivity at rest and found that highly creative people had increased connectivity in the attentional network (AN), the default-mode network (DMN) and a decrease in the salience network (SN). Our findings highlight the involvement of the AN, which is very scarcely mentioned in the literature. We therefore linked this network to creative potential, which is consistent with cognitive theories suggesting that creativity is underpinned by attentional processes. Furthermore, studying creativity with an approach based on a model of cognitive functioning seems more consistent with how connectivity data are processed.