Methane is a key molecule to understand the habitability of Mars due to its possible biological origin and short atmospheric lifetime. Recent methane detections on Mars present a large variability that is probably due to relatively localized sources and sink processes yet unknown. In this study, we determine how much methane could have been abiotically produced by early Mars serpentinization processes that could also explain the observed martian remanent magnetic field. Under the assumption of a cold early Mars environment, a cryosphere could trap such methane as clathrates in stable form at depth. The extent and spatial distribution of these methane reservoirs have been calculated with respect to the magnetization distribution and other factors. We calculate that the maximum storage capacity of such a clathrate cryosphere is about 2.1 × 1019-2.2 × 1020 moles of CH4, which can explain sporadic releases of methane that have been observed on the surface of the planet during the past decade (∼1.2 × 109 moles). This amount of trapped methane is sufficient for similar sized releases to have happened yearly during the history of the planet. While the stability of such reservoirs depends on many factors that are poorly constrained, it is possible that they have remained trapped at depth until the present day. Due to the possible implications of methane detection for life and its influence on the atmospheric and climate processes on the planet, confirming the sporadic release of methane on Mars and the global distribution of its sources is one of the major goals of the current and next space missions to Mars.