Brazilian police have reportedly issued a warrant for the arrest of Mario Marcelo Santoro in connection to the death of Cecilia Haddad in Sydney.
Mr Santoro flew back to his native country Brazil the same late April weekend the 38-year-old Brazilian mining executive's fully-clothed body was found in Lane Cove River.
Homicide police in Rio de Janeiro have issued a warrant for the arrest of the 40-year-old, who is Ms Haddad's former boyfriend, ABC News reports.
Fabio Cardoso, from Rio's homicide division, said police believe Ms Haddad was killed by asphyxiation.
"In April, by not accepting the breakup, he (Mr Santoro) allegedly killed her by asphyxiation by pressing her neck and dumping her body in the river," Mr Cardoso told the Seven Network in Brazil.
"We know he had the key to her house because he lived there for a while."
NSW Police last month issued a warrant for the 40-year-old's arrest and are requesting Interpol issue a 'red notice', which will alert 192 countries in case Mr Santoro flees his homeland.
There are concerns Mr Santoro will never be extradited to Australia to face charges because of Brazilian laws and customs.
NSW Police are translating a brief of evidence, including how they believe the murder unfolded at Ms Haddad's Ryde apartment, so it can be passed on to Portuguese-speaking Brazilian authorities.
Commonwealth Attorney-General Christian Porter said it was up to police prosecutors to decide if Mr Santoro would be tried in absentia if he did not return to Australia.
Australian journalists have been arriving in Brazil following news of the arrest warrant and have attempted to track down Mr Santoro at his apartment.
In a phone call he assured the Nine Network he would "reply" to questions about the murder but has yet to break his silence.
Mr Santoro did not respond to AAP's request for an interview following the murder.