Fatty acid methyl ester (FAME) is a relatively higher polar chemical compared to a hydrocarbon(hexane). This is the reason for better dissolution of FAME in chloroform. So you need a polar compound to make a dilute solution. You may try ethyl acetate as a solvent.
I have tried to give you a general guideline (polarity ) about the choice of solvent. It will also depend on the purpose of your experimentation.
I think due to the presence of some polar compounds, it not dissolved in hexane. You should put NH4OH on that (FAME). Try this with very minute sample.