It is understood the council's inquiries centre on internet use at a library in Greater Manchester.
The council has not taken formal disciplinary action against any individual during its investigation.
Merseyside police have already said no criminal offences were committed by the website itself.
But it is thought some officials plan private legal action against the author of Liverpool-Evil-Cabal, who uses the name "Tony Parrish", if he or she is unmasked.