At least once each year, the Council may take bids from privately owned garages for schedules of fees for towing and storing impounded vehicles or vehicles taken up because of illegal parking. Thereupon, the Council shall designate such of the bidders as shall be geographically located to tow and store such vehicles at a minimum cost in the event City facilities are not available for towing or storing vehicles to be impounded. The Chief of Police is hereby authorized to direct the public garage designated by the Council as aforesaid and located nearest to such vehicle to tow and store the same until disposed of as provided in this chapter. Such garage is hereby authorized to retain such vehicle until the fees for towing and storage on the basis of its bid shall be paid.