Evangelos Marinakis' Capital Ship Management (CSM) has reportedly ordered two aframaxes at Daehan Shipbuilding in China.
Brokers said the Greek owner will take delivery of the 114,000-dwt tankers in February and May, 2020.
No price was given for the deal. Recent orders have been priced at around $45m, however.
The company declined to comment on the transaction.
CSM is part of the Capital Maritime & Trading group and is listed with 24 tankers, bulkers and containerships.