A woman, aged 76, was walking home from a shop in High Green when she was targeted.
She told police officers that she was approached by a man who tried to talk to her as she walked to the Co-op in Newgate Close just after 11am on Tuesday, August 30.
As she walked home from the shop the same man approached the OAP again as she made her way towards Greengate Lane.
The oap was then pushed her to the ground and the man ran off with her handbag.
A South Yorkshire Police spokeswoman said: "Just after 11am on Tuesday, August 30, it is reported that the woman was walking towards the Co-Op along Newgate Close when a man has approached her and tried to engage her in conversation.
"The man left shortly after but as the woman, who is 76, made her way back from the shop via a footpath linking Greengate Lane and Newgate Close, the same man is said to have approached her again.
"It is then reported that the man pushed her to the ground before stealing her handbag and running from the area towards Greengate Lane.
"Police investigating the incident have released CCTV footage of a man who they would like to speak to.
"Do you recognise the man? "
Anyone with information should call South Yorkshire Police on 101.