The body of 35-year-old Paul Cunningham was discovered in a tenement flat in Dennistoun, Glasgow, at around 6.15pm on Monday.
An existing inquiry was upgraded to a murder hunt following a post-mortem.
Police said they are making extensive enquiries in the local area and studying CCTV footage.
The property was sealed off to allow police and forensic experts to make a detailed examination.
Police officers were seen at the entrance of the three-story sandstone tenement block in the quiet suburban street.
A police car was also on the pavement with a mobile police unit parked nearby.
Police said Mr Cunningham was last seen in the local area at around 11am last Friday by a friend, and police want to speak to anyone who saw him after that.
Officers are also working to get as much information as possible on Mr Cunningham, his lifestyle and the people he associated with.