Observations and inversion of the eigenfrequencies of free oscillations constitute powerful tools to investigate the internal structure of a planet. On Mars, such free oscillations can be excited by atmospheric pressure and wind stresses from the Martian atmosphere, analogous to what occurs on Earth. Over long periods and on a global scale, this phenomenon may continuously excite Mars’ background free oscillations (MBFs), which constitute the so-called Martian hum. However, the source exciting MBFs is related both to the global-scale atmospheric circulation on Mars and to the variations in pressure and wind at the planetary boundary layer, for which no data are available. To overcome this drawback, we focus herein on a global-scale source and use results of simulations based on General Circular Models (GCMs). GCMs can predict and reproduce long-term, global-scale Martian pressure and wind variations and suggest that, contrary to what happens on Earth, daily correlations in the Martian hum might be generated by the solar-driven GCM. After recalling the excitation terms, we calculate MBFs by using GCM computations and estimate the contribution to the hum made by the global atmospheric circulation. Although we work at the lower limit of MBF signals, the results indicate that the signal is likely to be periodic, which would allow us to use more efficient stacking theories than can be applied to Earth’s hum. We conclude by discussing the perspectives for the InSight SEIS instrument to detect the Martian hum. The amplitude of the MBF signal is on the order of nanogals and is therefore hidden by instrumental and thermal noise, which implies that, provided the predicted daily coherence in hum excitation is present, the InSight SEIS seismometer should be capable of detecting the Martian hum after monthly to yearly stacks.