Between 1.40pm and 7pm on December 1, officers said persons unknown forced entry to a property on Rotherham Road, Barnsley, causing damage.
The property had been searched and a quantity of cash and a bank card were taken during the burglary. The card was later used at several locations in Doncaster.
Police believe the men pictured could hold vital information and are appealing for them, or anyone who recognises them, to get in touch.
Anyone who has more information can call 101 or email firstname.lastname@example.org quoting incident number 261 of December 2.