Did a bit of digging and seemingly I`ts not compatible with my 5th gen i-pod.
There used to be an Apple device called the iPod Radio Remote which plugged into the Classic and added an FM radio tuner, but as far as I know it's long discontinued. I guess you may find one somewhere like ebay.
There's also a similar device from Gear4 called the BluEye, which will give the iPod both a radio tuner and Bluetooth - that seems still to be current, and Amazon has it at £22.99, but with only one left in stock.
I would post links, but all of a sudden the site seems not to be providing that facility, so I'll try to do it the old fashioned way, with HTML code
Gear 4 BluEye
Ah yes, that seems to work, but do much sure any device you decide to buy is compatible with whichever generation of iPod Classic you have.
Hope that helps