Female leaders remain a minority. Because leadership aspiration is a predictor of advancement, understanding stimulating conditions is important. A neglected perspective is the impact of organizational climate. We propose that cooperative climate can engender individuals’ motivation to contribute to the organization through leadership, and that leadership aspiration of women and men is differentially sensitive to interpersonal and collective aspects of cooperative climate. We argue that women are more disposed toward relational self‐construal and men toward collective self‐construal, and hence women's leadership aspiration is more influenced by the interpersonal element of cooperative climate whereas men's leadership aspiration by the collective element of cooperative climate. Results of a survey of N = 404 employed men and women supported both hypotheses.