If you can isolate the parasite's DNA, then you can get at-least part of it sequenced and then match the sequence against existing DNA sequence database using a software like BLAST. The closest matches will give you an idea of the species you are working with.
CARNEIRO J, PEREIRA F, AMORIM A (2012) SPInDel: a multifunctional workbench for species identification using insertion/deletion variants. Mol Ecol Resour. 12(6):1190-5