You can use solid phase extraction with C18 tube and eluation of organic compounds with methanol. SPE is the best procedure for extracting  organic compounds from water samples.

It is not clear what FA is?

Dear Soleya,

I am currently working on ethanol extract as well as water extract samples.My compound of interest are the fatty acids and sterol. I managed to detect in my ethanol samples but not yet on the latter sample. Thank you for your recommendation

You could use solid phase micro extraction and inject directly.

I think that the perfect solvents for dissolving fatty Acid are petroleum ether and n-hexane

I hope that good

Article Healthy cookies from cooked fish bones

Use n-hexane for extraction. Remove n-hexane. Apply esterification procedure using methanolic KOH and analyze using GC-FID.

Fatty acids are generally not that soluble in water, although the shorter chain ones will dissolve to some extent, and neither are sterols.  Generally both are soluble in organic solvents - hexane, ethanol, dichloromethane, chloroform etc.  For GC, unless you have a specialist column for looking at polar compounds (which fatty acids are), you will not get good results unless you derivatise them.  Methylation and silylation are both used.  This does alter the original sample but has the advantage of allowing them to be run on a general purpose, non-polar or slightly polar column.

The link below has some useful information about the analysis of lipids and there is a section on GC and lipids.

http://lipidlibrary.aocs.org/Analysis/?navItemNumber=19195