The problem of spontaneous magnetic field generation with nanosecond laser pulses raises a series of fundamental questions, including the intrinsic magnetization mechanisms in laser-driven plasmas and the understanding of charge-discharge processes in the irradiated target. These two issues are tightly bound as the charge-discharge processes are defined by the currents, which have in turn a feedback by magnetic fields in the plasma. Using direct polaro-interferometric measurements and theoretical analysis, we show that at parameters related to the PALS laser system (1.315 μm, 350 ps, and 1016 W/cm2), fast electrons play a decisive role in the generation of magnetic fields in the laser-driven plasma. Spatial distributions of electric currents were calculated from the measured magnetic field and plasma density distributions. The obtained results revealed the characteristics of strong currents observed in capacitor-coil magnetic generation schemes and open a new approach to fundamental studies related to magnetized plasmas.