Detectives are investigating the death of 26-year-old Sean Humphrey, who was discovered at 4am yesterday in Etive Street, Shettleston.
The murder probe was launched just 24 hours after the brother of the late gangland figure Tam 'The Licensee' McGraw was killed nearby.
Francis McGrow, 55, who was found dead in his home, was a member of the McGraw family, some members of which changed their surname from McGrow to McGraw.
Detectives investigating the death of Mr Humphrey said there was an earlier disturbance in the flat and they want to speak to two men who were in the street at the time.
Officers have been carrying out door-to-door inquiries and are checking CCTV footage, but they are appealing for anyone who may have information to come forward.
They are particularly keen to speak to two men seen in Etive Street at the time, one described as white, 20 to 25 years of age and wearing a dark top with orange markings, the other in his early 30s, wearing dark clothing.
Officers in charge of the two cases said the crimes do not appear to be linked and quashed any speculation that Mr McGrow's death was the result of serious and organised crime.
Detective Superintendent Robbie Allan said: "At this stage I have got absolutely no information that these deaths are connected.
"We have had these two deaths close to each other within 24 hours but there is nothing to indicate they are linked and nothing to link either to gangland crime.
"We are concerned that speculation that the deaths are related to gang activity may stop members of the public coming forward to provide information.
"We can ensure the safety of anyone who comes forward with information."
Millionaire Tam McGraw, known as The Licensee, died from a heart attack in 2007. He was a feared member of the city's underworld with links to the drug trade and extortion.
Mr McGrow was last seen by a family member at around 3pm on Saturday.
Police said he "rarely socialised" or left his home but he had a visitor to his flat in Hermiston Road, Springboig, on Saturday afternoon and Sunday morning.
Detective Chief Inspector Jim Kerr of Police Scotland said: "A man wearing a white tracksuit with blue flashes was seen nearby in Hollowglen Road at the Camlachie burn around 8.45am on Sunday.
"I am keen to trace him, those who went to Mr McGrow's flat or anyone who saw Mr McGrow between Saturday afternoon and Sunday morning."
Mr Allan was keen to stress that two suspicious deaths in such a short space of time is highly unusual.
Police patrols in the area have been stepped up to reassure worried locals.
Mr Allan said: "We have had two deaths in a short space of time in a small area and we understand that people in the area are concerned by what has happened.
"We have specialist units from across Scotland on board with both of these crimes.
"Police Scotland is absolutely committed to bringing those responsible to justice as quickly as possible."