A woman accused of bashing an elderly Melbourne dog walker could be charged with murder after her alleged victim died in hospital, four days after being attacked.

Le Le, 77, was found in a pool of blood and surrounded by her yelping dogs near her St Albans home on Thursday night and died in hospital on Monday afternoon.

She had been rushed to Royal Melbourne Hospital with head injuries after a passer-by raised the alert.

Police released news of her death on Tuesday.

St Albans woman Amy Tran, 30, faced Melbourne Magistrates Court on Monday charged with intentionally causing serious injury and was told charges could be upgraded if Ms Le died.

Magistrate Andrew Capell told Tran there was every chance the victim would die and her charge may be upgraded to murder or manslaughter.

The court was told Tran had a history of schizophrenia and drug use.

She was not known to Ms Le, and was arrested 100m from the driveway where the elderly woman was found, court documents showed.

Tran was denied bail and the matter was due to return to court on May 28, while police continue their investigation.

Detectives will set up an information caravan on Thursday night near the scene of the alleged attack as they continue searching for the passer-by, a man, who stopped to help.

He's thought to be of a Middle Eastern appearance with dark hair and aged about 50.