Senior officers from across the Police Scotland division have been brought in to solve the murder of Francis McGrow, 55, and Sean Humphrey, 26, whose body was found nearby less than 24 hours later.
Mr McGrow was the brother of Tam McGraw, who controlled a £30 million drugs empire and was known as The Licensee.
The feared member of the city's underworld, who had links to drug trafficking and extortion, died of a heart attack in 2007.
Officers 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.
However, extra officers have been put on patrol in the east end of the city where the attacks happened.
Mr McGrow, of Springboig, was last seen by a family member at around 3pm on Saturday afternoon.
Police said he rarely socialised or left his home but he had a visitor to his flat in the area's Hermiston Road on Saturday afternoon and Sunday morning.
McGraw's original name was McGrow, but he had it changed.
Detective Chief Inspector Jim Kerr 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 his flat or anyone who saw Mr McGrow between Saturday afternoon and Sunday morning."
Mr Humphrey's body was discovered at about 4am on Sunday in Etive Street, Shettleton. Detectives 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.
Det Supt Allan of the Major Investigations Team (MITs) said: "There have been two murders in Shettleston, Glasgow, in the past 24 hours.
"I would like to reassure local people that extra officers are now on patrol in their area and that additional detectives have been drafted in from throughout the force area to find those responsible for both attacks.
He added: "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."
He added that speculation they may be gang related could be unhelpful to the inquiries, adding that police ensured the safety of any potential witnesses.
Det Supt Allan was keen to stress that two suspicious deaths in such a short space of time is highly unusual.
Patrols in the area have been stepped up to reassure worried locals that the area is safe.
He 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 in their community."