A woman shot in the chest in her Melbourne home is understood to be the mother of a convicted police shooter with strong underworld ties.

The 52-year-old was fighting for life in Royal Melbourne Hospital's intensive care unit on Friday night after being shot in a Glenroy house at 11.50pm on Thursday.

She's believed to be the mother of Rodney Phillips, who last month pleaded guilty to recklessly causing injury, reckless conduct endangering life, criminal damage, arson and firearm possession.

3AW reported the woman shot is the mother of Melbourne gangland figure Rodney Phillips (Image: 9News)

Phillips had only been out of jail for three days - and his associate Sam Liszczak for just one day - when they drove to the house of a slain gangland boss' father in July, shot at it and threw Molotov cocktails.

Police pursued the pair as they left Carl Williams' father's house.

They fired into the officers' car, hitting Constable Ben Ashmore with multiple shots at close range.

The officer survived the attack and still has 11 pellets lodged in his skull.

The Glenroy shooting comes less than a fortnight before both men were due to be sentenced over the gangland attack.

A man who identified himself as the woman's partner told reporters he believed he knew who shot her.

Police are yet to charge anyone.