South Yorkshire Police's wildlife team have launched an investigation following an incident last week.
The two women were seen walking a dog - believed to be a German Shepherd - in a farmer's field near Finningley Gravel Pitts in Doncaster.
They were spotted at around 10am on November 15. Police were called with reports of livestock being distressed and dead in the area.
The following morning, a sheep was found dead in the field.
It is believed the dog had mauled the sheep to death while it was grazing in the field.
Wildlife officers investigating the attack are now trying to identify the two women, and have released images in a bid to track them down.
A spokesman for South Yorkshire Police said: "
Anyone with information that can help our officers is asked to call 101 quoting incident number 726 of November 15, 2021.
Support The Yorkshire Post and become a subscriber today. Your subscription will help us to continue to bring quality news to the people of Yorkshire. In return, you'll see fewer ads on site, get free access to our app and receive exclusive members-only offers. Click here to subscribe.