Damien Anthony Peters, 50, was last seen at Prince of Wales Hospital in Randwick at about 4:15 pm on Sunday.
According to reports, NSW police found his ankle tag about four hours later nearby.
According to reports, Peters pled guilty for murdering and dismembering two of his lovers in 2001.
For his crimes, he was jailed for 21 years with a non-parole period of 13 years, in 2002. He has been on parole since November 2016.
Police have described him as being of Caucasian appearance, about 175 to 185 centimetres tall, with a muscular build and short brown hair. He has a tattoo on his right upper-arm of a snake wrapped around a panther and various other tribal-style tattoos.
Police are recommending people call triple-zero if they see Peters.
This is a developing story.