South Yorkshire Police said a man and his young child were walking along Florence Avenue in the Aston area of Rotherham with their dog on a lead at 4pm when they were approached by a man.
The man then reportedly tried to snatch the lead out of the victim’s hand, but he held onto the lead and the offender fled the scene onto Mansfield Road.
The man is described as being around 35-years-old, 6ft tall and of a large build. He was wearing a black tracksuit and black baseball cap.
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DCI Jamie Henderson, Force Lead for Serious Acquisitive Crime said: “We know there is a great deal of concern about dog theft, nationally and locally, and we want to reassure you that investigations are ongoing.
"We understand how important dogs are to their families and know the impact this type of crime can have. We want to reassure you that we are actively carrying out enquiries linked to this attempted dog theft.
"We would encourage people to remain vigilant and report any incidents to us, as well as anyone you see acting in a suspicious manner. We will continue to act on this information."
Anyone with information can contact police on 101 quoting incident number 592 of 28 June.
South Yorkshire has seen a spate of dog theft cases in recent months, with the police constantly issuing fresh advice to pet owners.
In March, the force said it had dealt with 63 cases since last July in which a dog was stolen.