Prospection (mentally simulating future events) generates emotionally charged mental images that guide social decision-making. Positive and negative social expectancies - imagining new social interactions to be rewarding vs. threatening - are core components of social approach and avoidance motivation, respectively. Stable individual differences in such positive and negative future-related cognitions may be underpinned by distinct neuroanatomical substrates. Here, we asked 100 healthy adults to vividly imagine themselves in a novel self-relevant social scenario that was ambiguous with regards to possible social acceptance or rejection. During this task we measured their expectancies for social reward (e.g. anticipated feelings of social connection) or threat (e.g. anticipated feelings of rejection). On a separate day they underwent structural MRI; voxel-based morphometry (VBM) was used to explore the relation between their social reward and threat expectancies and regional grey matter volumes (rGMV). Increased rGMV in key regions involved in prospection, subjective valuation and emotion regulation (including ventromedial prefrontal cortex), correlated with both higher social reward and lower social threat expectancies. In contrast, social threat expectancies were uniquely linked with rGMV of regions involved in social attention (posterior superior temporal sulcus) and interoception (somatosensory cortex). These findings provide novel insight into the neurobiology of future-oriented cognitive-affective processes critical to adaptive social functioning.