The contract is overseen by INI's Inward Investment Division, which is responsible for attracting foreign direct investment (FDI).
The chosen agency will be tasked with highlighting the benefits of setting up a business in Northern Ireland.
Selling points for potential investors include low operating costs compared with some countries in Europe, a well-maintained infrastructure and an educated English-speaking workforce.
The statutory review puts London agency Stakeholder Communications and Dublin-based Drury Communications on alert. Both companies have worked for INI for the past three years, and said they would repitch for the new brief.
Fees for the contract - which is initially for one year, with the option to extend for a year - are undisclosed.