China, Vale's main market, has yet to give these ships access to domestic ports, forcing the world's largest iron ore producer to send its vessels instead to Italy, Oman and other destinations.
The vessel's arrival also comes amid rising concerns over the safety of these Valemax ships after a similar vessel, Vale Beijing, became disabled before setting sail on its maiden voyage.
The crew of the Berge Everest has not formally requested to stop in Singapore, said a port official, and may decide instead to anchor far offshore for supplies and to refuel.
Singapore's ports were wide and deep enough to handle the Berge Everest should the crew decide to dock, authorities said.
A spokeswoman with Singapore-based Berge Bulk, the owner of the vessel, was not immediately available to comment on the ship's voyage plans.
The Berge Everest, built by China's Bohai Shipbuilding Heavy Industry, is one of six mega bulk ships to be delivered to Vale so far this year.
The company wants to build a fleet of as many as 35 mega vessels to sharply cut the cost of delivering the steel-making ingredient to China.