Brenda Goudge was killed and her body dumped in the backyard pool of her Wantirna South home in July, 2011.

The 61-year-old was found by her daughter and a colleague when she did not arrive at work at the auto cable business she part owned.

Detectives are investigating whether she was killed by a former police officer who had served in the force for at least a decade. The former officer reportedly does not have an alibi for the night before Ms Goudge was found.

Homicide squad Detective Senior Sergeant Stephen McIntyre announced the reward on Tuesday, which would have marked Ms Goudge's 65th birthday.

Detectives are investigating whether she was killed by a former officer who had served in the force for at least a decade.

The former officer reportedly does not have an alibi for the night before Ms Goudge was found, Detective Senior-Sergeant McIntyre said.

He said the suspect had been arrested for the murder, but there was not yet enough evidence to lay charges.

"We have a suspect that we haven't been able to eliminate, we do not have sufficient evidence to progress this to a prosecution," he said.

"We believe someone will know something that will assist us, hopefully this additional money will be enough encouragement to come forward."

He would not reveal a motive for the murder, saying it would identify the suspect.

"This is a very sad case where a family has lost a much-loved mother and grandmother in tragic circumstances," he said.

Police believe Ms Goudge was beaten to death while she was in bed, possibly while she slept. There was no sign of forced entry to the family home in Newstead Way, where she had lived for 27 years, and it is not believed anything was stolen.

A $500,000 reward was announced in July, 2013. Ms Goudge's son Adam, who was joined at the announcement by his sisters Rebecca and Vanessa, said at the time that the killer's family should come forward.

"Understand what he's done," he said. "There's half a million dollar reward on the table for you to take."

In October 2012, police searched bushland near Howards and Blue House roads in Panton Hill for clothing linked to the case, and appealed for anyone in the area who had seen a four-wheel-drive to come forward.

Police reportedly forensically tested a silver 4WD the former officer sold after the murder.

"This is a baffling case. This victim is a person who lived a quiet life, lived home alone, worked every day, had no connections with anything where one might think this would happen," Detective Inspector John Potter said during the bushland search.

"Her family are baffled and we've undertaken to continue our investigations to give them some closure.

"This is an example of our progress in the case and we're hoping that today will bring us some answers."

with Tammy Mills