They stressed, however, that the two murders are not linked at this stage.
It is understood there is also no suggestion at this stage that Francis McGraw's death is connected with gangland activity.
The body of the 55-year-old was discovered at about 10am yesterday in his flat in Hermiston Road in the Springboig area of Glasgow.
Detective Chief Inspector Jim Kerr of Police Scotland, who is leading the investigation, asked anyone with information to get in touch.
He said: "Mr McGraw was last seen by a family member around 3pm on Saturday afternoon.
"He rarely socialised or left his home, however we know that he had a visitor to his flat on Saturday evening and then again for a very short time early Sunday morning.
"Also, a man wearing a white tracksuit with blue flashes was seen nearby in Hollowglen Road at the Camlachie burn around 8.45am on Sunday morning.
"I am keen to trace him, those who went to his flat or anyone who saw Mr McGraw between Saturday afternoon and Sunday morning."
Millionaire crime boss Tam McGraw died from a heart attack at his Glasgow home in 2007. Known as The Licensee, he was a feared member of the city's underworld with links to drug trafficking and extortion.
The second murder inquiry was launched after a 26-year-old man's body was found in a flat in Etive Street, Shettleston, Glasgow, at about 4am today.
Police believe 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.
Detective Inspector Fil Capaldi, of Police Scotland, said: "We know from our enquiries that there was a disturbance in the flat just before 4am this morning.
"We are keen to trace two men 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."
Detective Superintendent Robbie Allan said: "There have now 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.
"However, regarding speculation that the murder of Mr McGraw in Springboig is related to serious and organised crime, well this is extremely unhelpful and could indeed jeopardise our investigation. I would like to stress that there is nothing to suggest that is the case at this time.
"There is also nothing to indicate just now, that his death is linked to the murder enquiry ongoing in Etive Street, Shettleston."
Anyone with any concerns can contact police on the non-emergency number 101, Crimestoppers on 0800 555 111, or speak to officers that are on patrol in their area.