All electrical currents generate magnetic fields, so of course the short-lived electrical nerve impulses in the human body do so. But the generated magnetic fields would also be impulsive and equally short lived.
The data sheet for the LIS3MDL magnetometer specifies the sensor noise level as about +/- 3 to 4 mGauss (at the +/- 12 Gauss sensitivity setting), so it will not be straightforward to measure fields of 0-3 mGauss.