Toluene is a popular choice for FAME analysis. It really depends on YOUR specific samples and YOUR method (and their are a LOT of different methods). Select a suitable liquid that fully dissolves the sample and which does not interfere with the analysis (or detector) in preparation for injection.
BTW: FID is still a popular detector choice for GC biodiesel analysis, but expect differences in sensitivity, selectivity and LOD for MS and FID between both detectors as neither detection mode is universal or complete.
Biodiesel analysis of microalgal cultures using GC analysis are well documented. Try a keyword search on the web to find thousands of example methods, procedures, white papers, application notes etc for review. *Learning how to research a question on your own is one of the most important skills you can learn.
Consult a local professional chromatographer for hands-on help developing methods and running samples (to insure the methods and techniques used are appropriate and follow good chromatography fundamentals).
In gas chromatography-mass spectrometry (GC-MS) analysis of biodiesel or fatty acid methyl esters (FAMEs), methanol is generally not used as a solvent. This is because methanol is a polar solvent, and it can interfere with the separation and analysis of the non-polar FAMEs in the GC column. Additionally, methanol has a low boiling point, which can lead to issues with volatility and peak resolution in the GC analysis.
Hexane is the most commonly used solvent for dissolving biodiesel or FAMEs in GC-MS analysis. Similar to hexane, you can also use Heptane. chloroform can also be used as a solvent for FAMEs, especially if higher solubility is required.
Also, Toluene is another option, although it is less frequently used due to its higher boiling point compared to hexane and heptane