Non contact (contactless) AC or DC detection?
GMR sensors are very sensitive. (Hall sensors are not. However sometimes they call any magnetic sensor a hall sensor.)

You can approximately calculate the field next to a wire in mT.

You can look for a sensitive analog magnetic sensor

Then you can see what currents the sensor will be able to resolve from the data sheet information about resolution, temperature drift and noise (e.g given in uT).

My guess is you can't get it to work at 10mA, but can at 10A.

The sensor would be placed against the outer edge of standard flat TPS house wiring cable (Neutral wire side , not earth side) If you place it between N and phase, the field cancels.