Police have appealed for the public's help to find Wayne Ferguson, who was last spotted on May 4 at Ivanhoe in Melbourne's northeast.
A warrant was issued for his arrest on May 17 after he failed to tell police he changed his details, including his phone number and home address.
Officers have since searched the state extensively for Ferguson, but are yet to track him down.
The 57-year-old has never before failed to report to police after he committed rape offences against a person he knew as well as a stranger more than two decades ago.
"Because we've been speaking to a whole range of people known to him, we reasonably believe that he knows he's being looked for and he's actively avoiding us," Victoria Police Assistant Commissioner Chris Gilbert said on Friday.
Police described Ferguson as 180 centimetres tall with a medium build, blue eyes and a fair complexion.
He is mostly bald but has grey hair, and several tattoos including the word "dope" on his right knuckles, "Tony" on his left knuckles, "Mum Dad" in a heart on his upper right arm and a dragon head on the inside of his lower left arm.
He also had tattoos of a wizard on his left hand, two roses and a snake on his right hand, a scroll and hearts on his lower left leg and dragons on each side of his chest, police said.
Mr Gilbert said police believed Ferguson was putting his health at risk by not taking his medication while he was on the run.
"It is inevitable that he will be caught. It's a futile exercise to try and avoid apprehension and we ask him to consider that it's no life to be constantly looking over your shoulder," Mr Gilbert said.
Police did not believe there was an "escalated risk" of Ferguson offending, but the fact he was avoiding apprehension was a concern, he said.
Ferguson was from Melbourne's northern suburbs, and was known to frequent the city's CBD along with Sale and Traralgon in the Gippsland region, Mr Gilbert said.
Police urged people who saw Ferguson to call triple zero or Crime Stopper and not to approach him.
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