In everyday communication, children experience situations where their knowledge or perspectives differ from those of their communicative partner. The current study examined this issue in the context of real-time language comprehension, focusing on 5-year-old children’s ability to manage knowledge discrepancies about the identity of mutually visible objects. In Experiment 1, we examined 5-year-olds’ ability to manage privileged knowledge about an object’s identity. Using a referential communication task, we tested children (N = 60) in either a shared knowledge condition, where both the child and the speaker knew the identity of a visually misleading object (e.g., a candle that looks like an apple), or a privileged knowledge condition, where only the child knew the identity of the visually misleading object. Of interest was whether children could suppress private knowledge while processing a phonologically related word (e.g., “Look at the candy”). Results showed that children did not inhibit this knowledge during the early moments of referential interpretation. In Experiment 2 (N = 30), we contrasted the privileged knowledge condition in Experiment 1 with the more traditional scenario used to test common ground use, where the child knows the speaker cannot see certain display objects. Results confirmed a stronger ability to manage discrepancies in the latter case. Together, the findings demonstrate differences in children’s ability to manage distinct types of knowledge discrepancies during real-time language comprehension.