A member of the public disturbed two men inside the property on Dovecliffe Road, Wombwell, before they could take anything at 5.30pm on March 14.
A spokesperson for South Yorkshire Police said: “The offenders had first broken a padlock on the side gate to get into the garden, and then damaged the rear patio door to gain access to the property.
“No property was stolen due to the suspects being disturbed, and they fled.
“Enquiries have been proactively ongoing and officers are keen to identify the two men in the images as they may be able to assist with enquiries.
“Do you recognise them?
“If you have any information, please contact 101 quoting incident number 723 of March 14.
“Alternatively, you can stay completely anonymous by contacting the independent charity Crimestoppers via their website crimestoppers-uk.org or by calling 0800 555 111.”