One man has been arrested on suspicion of manslaughter and supplying drugs, the second on suspicion of allowing his premises to be used for the supply of drugs.
Police have not yet been able to reveal why John Paul Pearson, 35, of Bury Road, Gosport died because the initial post mortem was inconclusive.
They are still awaiting the results of further toxicology tests.
Detective Inspector Matt Cox said: 'The investigation is continuing and we are looking at all lines of inquiry.'
Mr Pearson's body was found on a footpath just off Old Road, Gosport, by a dog walker just before 7am last Friday.
After the body was found CID officers conducted door to door inquiries while uniformed officers swept the area looking for clues.
However, nothing was found which could explain the cause of death.
Many residents speculated that the death may have been drugs related and the footpath was branded a 'drugs hot spot.'
The two Gosport men have been bailed until February 19 next year.