A Hall cell insulated and pressed against the current carrying conductor will allow current to be monitored.
You will get a few zillion ideas from these images - each is hot linked to a page.
There are MANY hall sensors available which would do this job.
The items below are far from the cheapest but are better optimized for this task than many due to integrated "magnetic concentrators".
Digikey will happily sell you the devices below
Good article here
These novel, contactless current sensors consist of an integrated CMOS
Hall effect sensor covered by an additional thin, ferromagnetic layer
on its surface. This IMC layer acts as a magnetic flux concentrator,
providing a high magnetic gain that increases the sensor's
signal-to-noise ratio. The sensor is particularly appropriate for DC
and AC current measurement. Such measurements are characterized by the
need for ohmic isolation, very low insertion loss, fast response,
small package size, and low assembly costs. Typically, current sensors
are found in applications such as battery current monitoring, solar
power inverters, and power inverters that drive traction motors in EVs
(electric vehicles), and HEVs (hybrid electric vehicles). There is no
upper limit to the level of measurable current of IMC sensors, since
their output level depends only on the conductor's size and its
distance from the sensor.
Datasheet here for one version - SOIC8.