The body of Lauren M., 25, was discovered in her flat in Vienna's Wieden district in January this year, having been suffocated to death.
Firemen who broke down the door to her flat after her employer raised concerns found her half-undressed body lying face down on a mattress and surrounded by burning candles.
A police investigation led to a search for a Gambian failed asylum seeker thought to be living with her at the time, but who had apparently fled the city.
He was picked up nine days later at a refugee home in Switzerland and, after fighting extradition, was eventually deported back to Austria a few weeks ago.
In an interrogation by police, 23-year-old Abdou I. denied he is responsible for the murder and claims that he had already left Vienna at the time she was believed to have been killed.
He says he had already been deported to Italy in December and had made his way to Switzerland where he claimed asylum. His lawyer Astrid Wagner is now checking his story.
Police DNA evidence, however, shows his sperm was found on Lauren M,'s body and bed.
The Gambian says that he had a sexual relationship with the woman but did not live in her apartment, as had been claimed in earlier media reports. It had been thought Lauren M. was sheltering Abdou I. after his asylum application in Austria was rejected.
Lawyer Wagner has said she experts authorities to soon file a murder charge against her client.