Can air itself be used as a magnetic core in CT (Current Transformer)?
A good CT with a ferrite core is a challenge at this sort of frequency (and above) so I would definitely consider an air core especially if the only signal that can be picked up is the 13.56 MHz current. If you use a ferrite core it brings a different set of problems to the table like ferrite core losses and these might be excessive i.e. cause core saturation. 

Another problem with using a ferrite core is the leakage inductance; a CT relies on good coupling in order to project the burden resistor's impedance (via the turns ratio squared which is a massive impedance reducer) so that the wire through the centre of the CT sees a very low impedance. With excessive leakage you will likely get core saturation and inaccuracies in measurement.

So, it's worth considering an air core. For sure, there will be much greater leakage inductance and this will mean the voltage out (that supposedly represents the primary current) will be inaccurate but there won't be any saturation non-linearities. Yes, it will need calibrating and this might be a big issue but not impossible.

You could go the whole mile and use a sniffer coil to receive the magnetic field and do the math to determine the actual current flow. In effect a sniffer coil is the natural extension of a CT: -