We propose a novel statistical method to extend Fermi-LAT catalogues of high-latitude γ-ray sources below their nominal threshold. To do so, we rely on a recent determination of the differential source-count distribution of sub-threshold sources via the application of deep learning methods to the γ-ray sky. By simulating ensembles of synthetic skies, we assess quantitatively the likelihood for pixels in the sky with relatively low-test statistics to be due to sources. Besides being useful to orient efforts towards multi-messenger and multi-wavelength identification of new γ-ray sources, we expect the results to be especially advantageous for statistical applications such as cross-correlation analyses.