Kimberley McRae was found dead in her apartment on Mount St, Coogee on January 14.
The 69-year-old lived alone but was known to exercise in the local area.
In a statement on Monday, NSW Police said it was “aware” of the arrest of a 20-year-old man on the island of Aruba – a Dutch territory off Venezuela’s coast in the Caribbean Sea.
The man, nabbed last week, is reportedly from nearby Colombia and on a student visa.
“Detectives from the State Crime Command’s Homicide Squad are working with Commonwealth agencies to seek the man’s extradition to Australia,” police said.
“The priority for all Australian authorities is seeking the return of the man to face justice.”
Earlier this year, Homicide Squad Commander Detective Superintendent Danny Doherty said “Kim” was last seen at her unit on January 7 and they were treating her death as suspicious.
“Phone records show her mobile phone was in use the following afternoon January 8,” he said. “Her exact movements from the last time she was seen … and when her body was found seven days later is unclear.
“Kim had a distinct personal style with recognisable features and a wide circle of associates.”
He said they were aware she worked in the sex industry and may be known to some of her associates as Isabella, Samantha or Sabrina.
“Of course, we’d be keen to speak to anyone who has information or knowledge of Kim’s social activities,” Supt Doherty said at the time.