Bartle Bogle Hegarty London won BA’s creative account in the UK in 2014. Carat has handled media planning and buying for the group on a global basis since 2013.
An IAG spokesman said that a request for proposal has been issued to agencies, adding that the "procurement" review was "standard" practice "to ensure our business needs are met".
"IAG is constantly looking for greater efficiency and integration across the group," the spokesman said.
The company warned last month that revenues fell 4% in the traditionally strong summer quarter because of a "tough operating environment" and wants to keep a lid on "non-fuel" costs.
BA is regarded as one of the most prestigious UK advertising accounts and its decision to drop M&C Saatchi in 2005, after working with Maurice and Charles Saatchi for 23 years, is still remembered more than a decade later.