A body was found in an industrial bin on the Empress Road Industrial Estate, near Thomas Lewis Way, in the early morning of Easter Sunday, 8th April.
The body was burnt, and was found by the Hampshire Fire and Rescue Service during an incident involving a fire in the same place. The police were called just after 3am.
A post-mortem was due to be carried out later in the afternoon, but sources said the bad condition of the body was slowing the enquiry.
The Empress Industrial Estate is situated near to Bevois Valley, a popular area with students and residents alike.
No more information about the body has been released.
It is asked that anyone with any information or news of any suspicious activity in the area contact police on 101, quoting Operation Waterloo.
Information can also be given by calling the Crimestoppers charity on 0800 555 111 anonymously.