We present COPAINS (Code for Orbital Parametrisation of Astrometrically Inferred New Systems), an innovative tool developed to identify previously undiscovered companions detectable via direct imaging, based on changes in stellar proper motions across multiple astrometric catalogues. This powerful procedure allows for dynamical predictions of the possible masses and separations of unseen companions compatible with observed astrometric trends, marginalised over unknown orbital elements. Validating our approach using well-constrained systems, we found that our tool provides a good indication of the region of the parameter space where undetected secondaries may be located. Comparing the output of the code to the measured or expected sensitivity from various imaging instruments, this in turn enables us to robustly select the most promising targets for direct imaging campaigns searching for low-mass companions. Such an informed selection method promises to reduce the null detection rates from current programs and will significantly increase the current census of wide brown dwarfs and planetary companions to stars, which remain extremely rare in the surveys conducted so far.