The Constantine Angelopoulos-controlled company is understood to have booked four 160,000-dwt units, with options for two more, at Hyundai Heavy Industries (HHI).
Delivery of the firm vessels is said to be slated for 2016, while the suggested cost is around $68m each.
Repeated efforts to confirm the information with Arcadia proved unsuccessful.
The company already has four HHI-built suezmaxes — two constructed in 2004 and two in 2007.
