It is proposing to review drinks licenses to include the measure along with a ban on promotions outside the designated zone.
Under-18s would not be allowed inside the zone unless accompanied by an adult, and a security officer would have to be on duty during trading hours.
It also wants to limit the size of promotional material and to enforce the display of responsible drinking messages during promotions.
Councilor Mike Alcock, cabinet member for environment and infrastructure, said: “While we accept that all shops must be free to compete with each other on price, we feel that this still requires social responsibility and that measures must be taken to limit the impact that this has on our communities.”
The council has already carried out a review of on-trade premises’ licenses, including a limit to promotions.
Take-home retailers have been given until the end of December to respond to the latest proposals.