The campaigns will be predominantly focused on business travellers.
The review does not include the below-the-line account for bmi's low-cost airline, bmibaby.
Andrew Dufty, the head of marketing for bmi, has conducted credentials meetings with a number of below-the-line shops.
He is expected to shortlist six agencies to pitch. In the past, bmi has worked with Partners Andrews Aldridge to produce direct mail campaigns for its Diamond Club Service, as well as partnering with digital shops on an ad-hoc basis.
It is not known whether PAA will pitch for the whole account.
Last year, bmi launched its first TV campaign for six years, promoting its punctuality and frequent-flyer rewards.