Could elevated liver enzymes be a sign of liver cancer?

While it could: Enzymes (alt/ast) indicate liver cell injury/inflammation: hepatitis - from viruses to drugs to alcohol. Alk phos may point to duct obstruction. But these can all be up or none be up in cancer traveled to the liver.

No: Liver enzymes may be elevated for several reasons - but is almost never a sign of liver cancer. Elevated enzymes occur when the liver is damaged by alcohol, hepatitis, diabetes, fat, etc. It is important to note that damaged/cirrhotic livers are at greater risk to develop cancer. However, in this setting the elevated enzymes reflect the pre existing liver damage, not the development of cancer.