The anomalous magnetic moment g-2 of the muon is a precision measurement which exhibits a 3.5$\sigma$ deviation between theory and experiment, and in the next few years will be measured at Fermilab and J-PARC with even higher precision. The hadronic contribution to the muon g-2 ($a_\mu^HLO$) is the most important one after the pure QED contribution. It is however affected by a large uncertainty which dominates the error on the theoretical prediction in the Standard Model. We propose a novel approach to determine the leading hadronic corrections to the muon g-2. It consists in a measurement of the effective electromagnetic coupling in the space-like region at low-momentum transfer, which provides direct sensitivity to $a_\mu^HLO$. We discuss the possibility to perform this measurement with the Bhabha process at flavour factories as well as by scattering muons of 150 GeV (currently available at CERN North area) on atomic electrons of a low-Z target. These direct measurements will provide an independent determination of $a_\mu^HLO$, competitive with the time-like dispersive approach, and consolidate the theoretical prediction for the muon g-2 in the Standard Model. It will allow therefore a firmer interpretation of the measurements of the future muon g-2 experiments at Fermilab and J-PARC.