The economic performance and to a certain degree the stability of modern society depend on the reliability and durability of concrete infrastructure. Therefore, maintenance of infrastructure remains one of the primary core tasks. If damage at an early stage is detected and precautionary measures are applied, maintenance costs can be significantly reduced, and lives can be saved by preempting failure. Concrete damage at an early stage is characterized by microcracks, much smaller than the aggregate size whose detection is not possible using conventional ultrasonic (US) monitoring. However, the multiple-scattered late arriving US signals (i.e., coda signals) contain rich information that detects weak changes. While the high precision and sensitivity of the coda signals can be used to identify precursor damage events that precede catastrophic failure, extracting this information is challenging. In this contribution, a multi-scale approach combining computational modeling and machine learning techniques are used to simulate the identification of damage level in concrete specimens using coda wave interferometry. Concrete damage is simulated using a reduced order multiscale model that combines continuum micromechanics, the integral form of the Lippmann-Schwinger equation solver for the strain field at the mesoscale and machine learning. Data from wave propagation simulations are used to compute the relative velocity change i.e. a measure of weak change in the material using coda wave interferometry. The results of the analysis and the potential for estimating precursor damage directly from ultrasonic signal measurements are discussed.