The attacks took place in East London.
One victim was punched to the ground and left with a black eye after the assault in Walthamstow.
The attack took place on 4 November as the victim, a 31-year-old man, walked along Hoe Street with two friends.
He said they were approached by three men they did not know and that he was punched in the face as well as being subjected to anti-gay slurs.
A second victim was told “you are not welcome” after being attacked as he walked the high street with his husband after a night out.
The 47-year-old man was attacked while walking along Walthamstow High Street on 8 October after they had been on a night out in Walthamstow Village.
According to police, two men approached the couple, asked if they were gay and asked if they could take a photo before walking away.
But then the suspect allegedly grappled with the victim and told him “you are not welcome”.
Two e-fit drawings have been released by the Metropolitan Police in London based on descriptions from both of the victims.
Scotland Yard has said the victims provided detailed descriptions.
A spokesman said: “Based on these descriptions and the locations where the assaults happened, officers have not ruled out the possibility that the attacks may well have been carried out by the same man.”