A homeless man will face court on Thursday for allegedly collecting Sarah Gatt's Centrelink payments before her body was found in her bathtub.

Police found the 40-year-old woman's badly decomposed remains in her Lambeth Street, Kensington, unit on January 3 last year, after they had gone there to issue a witness summons to her for court.

It's believed Ms Gatt's body had been left in her bathtub for eight months.

Nobody has been charged over her death, but a 52-year-old man of no fixed address will front the Melbourne Magistrates Court on Thursday for allegedly collecting her welfare payments.