That's a good question. All the places I've purchased glycerin from just state vegetable glycerin but don't give any further information. I get it from Soapers Choice, Natures Garden or WSP. You may need to contact them.
If I'm not mistaken, if you want palm and soy free, the only other option is coconut. However, in my experience, the coconut is usually used in addition to palm, so you would have to contact the supplier for that information.