It's understood chemistry sessions with agencies have taken place and the process is expected to be completed in September.
It's currently unclear whether the retailer will continue with the dual-agency approach.
Ingenuity London has been helping Morrisons with the agency selection process. Morrisons, The Academy and Cirkle all declined to comment.
Morrisons, which has almost 500 stores, has been in the news this week after announcing a tie-in with Amazon to allow consumers to buy its products via the online shopping platform. The supermarket chain has also been trialling the removal of plastic bags from its stores in favour of paper alternatives.