The man pictured is believed to be one of two culprits who went to a house in the East Bowling area of the city at around 1pm on November 20 and offered to do some work on the occupants’ guttering.
He asked the occupants to go to the back of the house with him to look at the guttering, while a second male entered through the "insecure" front door.
The occupants, who are both in their nineties, later discovered that a safe had been taken.
The safe is believed to have contained personal items and around Â£1,500 in cash.
Detective Constable Sharon Cooper, of Bradford District CID, said:“This was a despicable crime carried out against a vulnerable couple and we are keen to hear from anyone who may recognise this male, or anyone else in the East Bowling area or Bradford District who may have been visited by these people under similar circumstances.
“We would also like to take this opportunity to remind people to keep their doors locked at all times to help prevent this type of offence.
“If you are not sure if a cold caller is genuine ask to see some identification or ask for their name and a contact number for their company. Genuine callers will not mind waiting while you check out their details.
“If you are still not sure do not open the door and report the matter to police on the 101 non-emergency number.”
The culprits are described as white males.
One of them was believed to be in his forties and is described as being of large build.
He was believed to be around 5ft 10ins tall and was wearing a blue beanie style hat and an anorak with a jumper underneath.
The second is described as being in his late twenties with medium length jet black hair.
He was of slim build, around 5ft 7ins tall and was wearing all black clothing.
Both are believed to have arrived and left the property in a blue car, which had a roof rack and ladders on it.
Detectives believe a third sculprit could also be involved after witnesses reported another male getting out of the car in East Bowling.
Anyone who recognises the male or who may have information about the offence is asked to contact Bradford District CID on 101, quoting crime reference 13170542721.
Information can also be reported anonymously to the independent charity Crimestoppers on 0800 555111.
More information about burglary and how you can prevent it can be found at www.westyorkshire.police.uk/burglary