The woman was targeted after she used the cash machine at Tesco on Dewsbury Road, Beeston, at around 8.30pm on Friday May 6.
She started to walk along Fairford Avenue where she was followed and approached from behind.
The suspect tried to steal her handbag and knocked her to the ground in the process. He fled empty-handed and ran off towards Dewsbury Road.
He is described as a 35-year-old 5ft 10in tall Asian man of slim build and unshaven.
He was wearing a black wax coat with the hood up, dark blue jeans and dark trainers.
Police Constable Alex Daniels of Leeds District Police, said: “The victim was shaken by this incident but thankfully she was unharmed. We are releasing this image in the hope that members of the public can identify this man.
“Anyone who recognises the man in the E-Fit or has any information about this incident is asked to contact myself at Leeds CID via 101 quoting reference 13160194179.”