The victim -- a well-known journalist and media personality -- is said to be "deeply traumatised" by the incident which happened at around 3am on June 8 last.
Gardai say that the pair are believed to have threatened the journalist with a knife, punched him in the face and kicked him before stealing his iPhone worth €400.
The 46-year-old victim was eating at a city-centre restaurant when he was approached by two thugs who engaged in conversation with the man for some time before threatening and attacking him.
The journalist ran from the popular restaurant, but the pair chased him and tripped him up before laying into him a second time.
A source explained: "They asked him where he had been earlier that night and he told them that he was at a gay event in the Dandelion bar."
The taller of the men who features in the CCTV images is the suspect who gardai believe armed himself with a knife during the incident.
The journalist was punched and kicked a number of times during the attack.
A senior source said today: "This is being treated as a homophobic attack -- gardai are 100pc confident of that."
Detectives are probing whether the attackers may have been responsible for three similar robberies in recent times.
A source pointed out: "The victim was left with severe bruising to his body, cuts to his forehead and knees as well as sore ribs after the attack and he is extremely shaken over the incident.
"This is a well-known openly gay man who has travelled the world but has never experienced anything like this. It really was a brutal attack."
There were five homophobic attacks in Dublin city centre last year.
Earlier this year, TV star Brendan Courtney (39) was attacked while on a night out close to where last month's incident happened.
In that gay-bashing incident, Mr Courtney was in Dublin city centre after a night out in February when a man in his 20s ran up, hit him in the face and called him a "queer" before fleeing.
However, he is sure the man will get away with the attack.
He said: "I was with eight friends and he got in a punch and left me with a black eye.
"They haven't caught the guy and they won't as the CCTV footage is at the wrong angle.
"The cops have been great but all they can do is try to match descriptions, and without the CCTV it's too tough."
Anyone with any information is asked to call Pearse Street Station at 01-6669000 and the Garda Confidential Line 1-800-666-111.