WDMP, which was appointed to handle a customer relationship marketing project for the tour operator last December, is involved in the review, which is due to conclude by the end of August.
The pitch will not affect WDMP's relationship with Thomson, which merged with First Choice via its parent company TUI in April 2007.
First Choice is looking for an agency to handle all of its CRM campaigns. The activity will seek to increase brand engagement, drive customer retention and encourage lapsed customers to return.
A First Choice spokesman said: "The intention is to formally secure the services of a retained agency to help shape First Choice's CRM strategy and creative development."