Croydon Council is proposing to fix persistent thieves with GPS trackers and exclude them from parts of the borough.
Executive Mayor Jason Perry said he is examining how the ankle tags could be used to tackle prolific criminals.
He hopes the technology will deter repeat offending.
“Shoplifting is not a victimless crime,” Mr Perry said.
“It threatens people’s livelihoods, drives up prices for honest customers and leaves shopworkers facing intimidation and abuse simply for doing their jobs.
“Our businesses have had enough of prolific offenders repeatedly targeting their shops, and so have I. My message is clear - that if you come to Croydon to steal, you should expect consequences.
“Zero-tolerance means backing our businesses and using every legal tool available to protect them. GPS tagging could help us monitor persistent shoplifting offenders, enforce exclusion zones and prevent the same people returning time and again to cause more harm.”
There were almost 4,800 reported shop thefts in Croydon town centre in the last 12 months and 5,043 the year before.
Council officials met earlier this year with Sussex Police after the force was the first area in the UK to successfully pilot the ankle tags in this way.
Two prolific offenders - Barry Farthing, 41, and Victoria Hale, 50 - were ordered to wear the tags for a year and avoid specific areas containing supermarkets in East Sussex.
Croydon town hall said it has also had discussions with the Met and technology providers about the rollout but funding for the scheme is yet to be secured.
Mr Perry added: “We will continue working with the police, businesses and technology providers to develop this pilot and make Croydon a safer place in which to work, shop and live.”
Benedict Selvaratnam, managing director of Freshfields Market in Croydon and co-founder of Croydon Business Association, said: “Shoplifting has a significant impact on businesses, particularly retailers.
“It is not simply the financial value of the goods being stolen. There is also the cost of additional security, and the pressure it puts on staff, and morale.
“Persistent offenders make staff feel unsafe at work, and many businesses feel frustrated when the same individuals return repeatedly.
“I would support tougher and more effective action against persistent offenders, including the appropriate use of GPS tagging. Where individuals repeatedly target shops and businesses, there needs to be a meaningful deterrent and a way of preventing that cycle from simply continuing.”