Advice/ techniques in non-invasive nA-range current reading
As Damien rightfully mentioned, nA is not the conventional territory of contactless sensing.
However, Magnetoencephalography does this for even smaller current. nA should definitely be possible if you can get close to the current line. If you can get within 1 mm of the line, the magnetic field will be 1µA/m which is about 1.3 pT.
To detect such small magnetic fields, the conventional sensors based on the normal Hall effect are not sensitive enough (not in a straightforward way) but sensors based on ferromagnets are. There are scientific demos of even pT sensitivity and below for such sensors. The sensors that come to mind to possibly detect this are planar Hall sensors and fluxgate sensors allow such precision. To select which sensor might suit you best, it is very important to consider the exact geometry of your current line and sensor. Using a small ring core around the current line with a planar Hall sensor instead of the usual semiconductor Hall sensor should do the trick.
But I am not aware of any commercial device that offers this.
Edit: it should be mentioned that the earth magnetic field is about 50 µT. So nulling + a very stable mount or better yet: magnetic shielding is absolutely mandatory to detect such small current in a non-contact way.