The car manufacturer has approached several agencies to pitch for the business, which includes all direct and customer relationship marketing for the Korean car marque.
It is not known whether the incumbent, Carlson Marketing, will repitch. The agency has held the account for the past four years.
Hyundai appointed Carlson in 2003 following a three-way shoot-out against Clark McKay Walpole, WWAV Rapp Collins and Dunnhumby Cinnamon.
Hyundai, combined with sister company Kia, is the world's sixth-biggest car manufacturer, and sells more cars than Honda.
However, it will be looking to increase its presence in the European market, where Hyundai and Kia combined only have a 3 per cent share.
Hyundai has already begun to increase its sales capacity across the continent, investing EUR1 billion in a new plant in the Czech Republic.
Hyundai denied it was holding a review. Carlson was unavailable for comment.