Agencies have been contacted with a request for information ahead of a pitch process run by AAR. There are no incumbent agencies.
The chain, which sells FMCG brands as well as groceries, has been in rapid expansion mode since floating on the London Stock Exchange in June 2014.
A significant stake in the company was bought by private equity fund Clayton, Dubilier & Rice in December 2012, and Leahy joined B&M’s board of directors.
Last year it opened 47 stores in 26 weeks, compared to 20 stores the year before.
The company’s chief executive, Simon Arora, admitted in November 2015 that the expansion had caused "operational issues", which left shelves empty and warehouses unable to cope.
B&M did not respond to a request for comment from Campaign.