Pre-reading abilities are predictive of later reading ability and can be assessed before reading begins. However, the neural correlates of pre-reading abilities in young children are not fully understood. To address this, we examined 246 datasets collected in an accelerated longitudinal design from 81 children aged 2–6 years (age = 4.6 ± 0.98 years, 47 males). Children completed pre-reading assessments (NEPSY-II Phonological Processing and Speeded Naming) and underwent a diffusion magnetic resonance imaging (MRI) scan to assess white matter connectivity. We defined a core neural network of reading and language regions based on prior literature, and structural connections within this network were assessed using graph theory analysis. Linear mixed models accounting for repeated measures were used to test associations between children’s pre-reading performance and graph theory measures for the whole bilateral reading network and each hemisphere separately. Phonological Processing scores were positively associated with global efficiency, local efficiency, and clustering coefficient in the bilateral and right hemisphere networks, as well as local efficiency and clustering coefficient in the left hemisphere network. Our findings provide further evidence that structural neural correlates of Phonological Processing emerge in early childhood, before and during early reading instruction.