Arunkumar Tikku, 62, was found murdered in the bathroom of his first floor apartment in the plush Lokhandwala Complex late on Saturday night.
The sexagenarian bore six to eight stab wounds on his abdomen and a computer cord was tied around his neck.
"Actor Anuj Tikku, who is the son of Arunkumar, and his friend Dhananjay Shinde, who is suspected to be one of the two paying guests in his flat, were picked from Chiplun area of Ratnagiri," a crime branch official said.
"We are looking for one more person. The mystery behind the murder can be solved after picking up the third person," the official added.
A businessman based in Delhi, Tikku owned three flats on the first floor of the high-rise Samartha Aangan-3A.
Police said the knife, which was used to stab Tikku and was recovered from the spot, has been sent for fingerprint analysis.
According to police, two paying guests had moved in to live with Anuj only a fortnight ago. The victim was a widower and had recently arrived in the city to take his son back to Delhi as he did not have a job.
After the incident, Anuj and the two tenants went missing, prompting the police to suspect their role in the murder.
According to police sources, a witness, who was walking towards his car at the time of the incident, claimed to have seen a man, who could be Arunkumar, struggling near the window of his flat in the building while his attacker was stabbing him.
The witness alerted the neighbours and security supervisor who had gone to Tikku's flat (no 101) and knocked on the door, police sources said.
According to them, one of the two men clad only in jeans, had opened the door and pulled the security guard inside.
The witness also rushed inside the flat sensing that something was amiss owing to the suspicious behaviour of the two.
"There were blood stains on the bodies of the two suspects inside the room, the witness claimed," the police officer said.
"When the witness further questioned the two, they said that they were watching an IPL match, during which, they had a fight and because of that there were blood stains," the officer said quoting the witness.
The deceased owned three flats -- 101, 102, 103-- in the high-rise and the two, whom the witness was talking about, could be paying guests, police said.