Police were called to the courtyard of a building in Conder Street, Burwood about 9.45am, where they found a man’s body.
Then, the body of a woman with stab wounds was found inside a unit in the complex.
Both have yet to be formally identified, police said.
Superintendent Christine McDonald, Commander, Burwood Police Area Command said it was “too early to say” if the deaths were “domestic-related,” or if what happened was a murder-suicide.
Supt McDonald said the man had ankle injuries and it was possible he had jumped from a unit.
Police are still trying to work out who the pair are, but said a woman was seen on CCTV walking towards the apartment this morning.
“We don’t know who they are at this stage,” she said.
Police have found a weapon.
Supt McDonald appealed for anyone who saw or heard anything to contact police.
Crime scenes were set up and officers are investigating.