The airport operator issued a tender earlier this week, with agencies having until the beginning of next month to register their interest in pitching for the account.
An agency is expected to be appointed to the business by the end of the year, with the successful shop holding a contract for an initial three-year period, with an option to extend it for a further 12 months.
The agency will be responsible for developing the WorldPoints scheme, which rewards consumers for shopping at BAA's UK airports.
Rewards include airport shopping vouchers, car-park discounts, Airmiles, and frequent-flyer points with airlines such as British Airways and Virgin Atlantic.
BAA does not currently have an agency on the account. However, it has previously worked with shops such as Libertine London and Naked Communications on advertising projects for specific airports.
Last month, the organisation retained Carat for its media planning and buying for Heathrow Airport after a year-long statutory review.
BAA operates six airports in the UK, including London Heathrow, London Stansted, Glasgow International and Southampton.
It sold London Gatwick to Global Infrastructure Partners for £1.5 billion in 2009.