We present a survey of M31 novae in quiescence. This is the first catalogue of extragalactic systems in quiescence and contains 37 spectroscopically confirmed novae from 2006 to 2013. We used Liverpool Telescope and Faulkes Telescope North images taken during outburst to identify accurate positions for each system. These positions were then transformed to archival Hubble Space Telescope (HST) images and we performed photometry on any resolvable source that was consistent with the transformed positions. As red giants in M31 will be resolvable in the HST images, we can detect systems with red giant secondaries. There are only a few confirmed examples of such systems in our Galaxy (e.g. RS Oph and T CrB). However, we find a much higher portion of the nova population in M31 may contain red giant secondaries. For some novae, coincident HST images had been taken when the nova was still fading, allowing us to produce light curves that go fainter than is possible to achieve for most extragalactic systems. Finally, we compare the M31 and Galactic quiescent nova populations.