Glycine (NH2CH2COOH) is the simplest amino acid relevant for life. Its detection in the interstellar medium is key to understand the formation mechanisms of pre-biotic molecules and their subsequent delivery onto planetary systems. Glycine has extensively been searched for toward hot molecular cores, although these studies did not yield any firm detection. In contrast to hot cores, low-mass star forming regions, and in particular their earliest stages represented by cold pre-stellar cores, may be better suited for the detection of glycine as well as more relevant for the study of pre-biotic chemistry in young Solar System analogs. We present 1D spherically symmetric radiative transfer calculations of the glycine emission expected to arise from the low-mass pre-stellar core L1544. Water vapour has recently been reported toward this core, indicating that a small fraction of the grain mantles in L1544 (~0.5%) has been injected into the gas phase. Assuming that glycine is photo-desorbed together with water in L1544, and considering a solid abundance of glycine on ices of ~1E-4 with respect to water, our calculations reveal that several glycine lines between 67 GHz and 80 GHz have peak intensities larger than 10 mK. These results show for the first time that glycine could reach detectable levels in cold objects such as L1544. This opens up the possibility to detect glycine, and other pre-biotic species, at the coldest and earliest stages in the formation of Solar-type systems with near-future instrumentation such as the Band 2 receivers of ALMA.