The search had narrowed to one after about 50 people had been questioned, an official said, adding that the main suspect was being interrogated.
The accused is believed to be a notorious robber but officials said they could confirm the information only after thorough investigations.
The 27-year-old Spanish musician was raped and robbed by the unidentified man early Monday. Police had earlier said she was a German national but later clarified that she is of Spanish origin whose parents live in Germany.
Piecing together the horrific details, police sources claimed the man entered the victim's flat, raped her twice and later ordered the victim to take a bath. He is also believed to have wiped off finger prints and traces of evidence that might have been left in the due course.
The accused later fled the scene with cash in Indian and foreign currency and a few valuables belonging to the victim.
According to Additional Commissioner of Police Vishwas Nangre-Patil, the preliminary medical examination of the victim has confirmed sexual assault. The prime motive was robbery, he said.
Quoting the FIR filed by the victim, Nangre-Patil the accused had held the victim at knife-point after he entered the apartment through an open window.
"The accused threatened her with his knife and raped her and later fled the apartment with some of her belongings and cash in foreign and Indian currency," he said.
This is the second such incident in the last 10 days. On Oct 28, two unidentified youths had allegedly attacked and molested a 21-year-old Russian woman at Worli Seaface in south Mumbai.
The woman was left with a bruised lower lip after one of the accused bit her. She had left the city without filing a police complaint. However, the cops took suo motu cognisance of the matter and filed a case against the two unidentified men.