The Game Group, which operates six stores in Edinburgh, applied to the city council for an exemption to laws which prevent firms from selling on stock within 48 hours.
The move is expected to allow the firm to be more flexible with its stock, and sell on games as soon as they become available.
But police warned that although there is no evidence that Game is involved in the acquisition of stolen goods, the nature of the industry meant goods are regularly stolen and sold on to unsuspecting businesses.
Current traders laws under the Civic Government (Scotland) Act mean that police have 48 hours to investigate the theft of goods before they can change hands.
The police licensing department’s inspector warned: “Should members of the criminal fraternity become aware of this exemption it is possible that the premises would be utilised by such persons.”
He said the 48-hour rule was generous enough and should not hinder business.
Officers said a number of second-hand businesses have been seeking an exemption recently and urged councillors to refuse them.
He added: “I would urge the committee to refuse all such applications, as the waiving of the 48-hour rule could potentially hinder police enquiries and result in lost opportunities when investigating thefts and the handling of stolen goods.”
Game, which has stores at the city’s five main shopping centres as well as in Princes Street, also applied to the Licensing Committee to sell games to under-16s, which police recommended against unless with an adult.
It applied to install a new record-keeping system, as the stores have previously been pulled up by officers for not keeping records of customers who buy second-hand goods.
The decision was put off until November while Game examines its applications.
A Game spokeswoman said: “This application is just routine to ensure we deliver the best service to customers and we will work with the authorities to address any concerns they may have.”
The firm said the move was not part of a national strategy.
City centre councillor Joanna Mowat, also a member of the Licensing Committee, said: “This is something that the police recommend we do and it is entirely about the reselling of stolen goods.
“I can understand the shop wants to move their stuff and they don’t want to keep goods for 48 hours, but actually it’s about protecting the customer who goes in and knows what they’re buying is legitimate.