A decision is yet to be made on whether a dog that fatally attacked its elderly owner southwest of Sydney will be put down.

A 72-year-old woman died after she and her 74-year-old husband were attacked by their American staffordshire terrier at their Wilton home on Thursday.

The elderly couple was taken to Liverpool Hospital where the woman later died and her husband remains in a stable condition.

The dog was seized by Wollondilly Council rangers and won't be euthanised at this stage, AAP understands.

The council is working with the family to follow the standard process for managing a dog attack, a spokeswoman said in a statement on Friday.