The Luton-based company is understood to have contacted a number of advertising agencies as it looks to raise its profile in a highly competitive sector.
Monarch currently offers a range of travel and leisure services, including low-cost flights, hotel and villa deals and car hire services.
The company flies to more than 50 destinations worldwide, carrying around 6.5 million passengers each year.
Monarch currently uses a number of local agencies to handle its marketing activity, including Butterfield Morris Bushell, Milton Bayer and Radius.
Carat is the incumbent on its media planning and buying business, and has worked on the account for more than four years.
In October last year, Monarch also appointed WDMP to oversee its customer relationship marketing activity. The agency’s relationship with Monarch is unaffected by the review.