The review is being handled by the AAR. Chemistry meetings are expected to take place next week with a shortlist being drawn up by the end of the month.
The company is looking for an agency to handle a two-part project, the first of which will be based around creating extensive in-store promotions in the run up to Christmas.
The second will see the winning agency briefed to rebuild the company's website and boost its online presence.
Game currently works with Dave, the Engine-owned business consultancy, but it is unclear whether it will be affected by the review.
The business has grown from 11 stores in the UK in 1991 to 1,161 stores across Europe, including 400 in the UK and Ireland.
Last year, the company's revenue was £1.1 billion with a gross profit of £275 million.
Earlier this month, the retailer announced plans to compete head-to-head with its suppliers by launching its own-brand computer games.