The account is currently held by D'Arcy New York, although D'Arcy London has taken responsibility for producing the organisation's UK campaigns in the past. Earlier this year, the agency created three 20-second TV executions as part of an integrated campaign to woo travellers back to the island.
However, D'Arcy New York will not be taking part in the pitch, having declined on behalf of all its regional operations.
The pitch will be held in the Bajan capital Bridgetown. The account is thought to encompass TV work, as well as press and outdoor briefs.
The move casts doubt upon the position of D'Arcy's direct marketing arm, Arc, as the Barbados Tourism Authority's below-the-line agency.
However, the organisation's media account, which is handled by MediaVest, is not thought to be affected.
The UK and the US supply more tourists to Barbados than any other countries, but US interest in the Caribbean as a holiday destination has waned over the past three or four years. Signs of a revival were tempered last year by 11 September and the subsequent war on terrorism.
The importance of the UK to Caribbean tourism has grown over the past two years as the euro's continually weak performance against the US dollar has rendered cross-Atlantic travel more expensive for the rest of continental Europe.