The flames and smoke "were too much" for the man and woman and they were unable to save the 71-year-old victim on 19 September, police said.
He was pronounced dead at Wellington House sheltered and retirement housing complex in Sandy Lane, Stretford.
The pair "ran further inside" than others who helped evacuate residents.
Police are appealing for them to come forward following the fire at about 16:15 BST to help with inquiries.
The man is described as Asian with a large build. He was wearing a blue bandana with large white spots or motifs.
The woman is described as white with long brown tied-up hair. She was wearing a bright red or pink sleeveless top with a black pattern on the front.
Det Sgt Andy Darnton said: "We would like to appeal for these people to come forward not only to assist with our enquiries but also to thank them for their heroic actions."
An investigation to establish the cause of the blaze is under way.
Two people who tried to smash through a door with a fire extinguisher to rescue a man trapped in a flat blaze in Greater Manchester are being sought.