Rank, which also owns betting outfit Blue Square and Grosvenor Casinos, is understood to have a budget of £5m for media in 2008 and spent £1.4m promoting Mecca Bingo in 2007, according to figures from Nielsen Media Research.
The company is believed to be on the verge of appointing a media agency for Grosvenor Casinos. That decision will be followed by a review of the Mecca Bingo account.
Incumbent Mediaedge:cia is believed to be repitching, while several other agencies have been approached by the gaming firm.
Rank Group, which is preparing to announce reduced year-on-year profits for 2007 this Friday, was unavailable for comment as Media Week went to press.
Rank Group has already warned that profits for 2007 will be "significantly lower" than those for 2006, with the smoking ban introduced last July being blamed in large part for the downturn.
Research company Mintel has forecast that bingo will suffer more than other trades because of the smoking ban.
It has estimated that the bingo market declined 12% in 2007 to be worth less than £2.5bn annually.
CIA Medianetwork, one of Mediaedge:cia's predecessors, landed Rank Group's account in June 1997 and has had a relationship with it ever since.