If you're wanting to measure AC current through a wire, then the lines of
magnetic flux from the current must pass through the loops of wire in your
sensing coil. Since flux lines are concentric around a wire, they are not
passing through your loops, but are running parallel to them. If you wrap your
sense coil around a plastic toroid, and then run the ground wire through the
toroid opening, you'll have the geometry you're looking for. You may still
need some sort of amplifier, and wether or not your meter's frequency response
is limited or not may just depend on the meter, but rewinding the coil would
seem to be the place to start.

Wes B.