"The first phase of the tender is complete with three of the world's top port administrators submitting bids," OLTH said.
Dubai ports bid jointly with Piraeus Bank and construction firm Aktor.
"The interest of these three investors exceeds any optimistic projection, they have long experience in the world ports industry," Greek Merchant Marine Minister George Voulgarakis said.
Last week, Piraeus Port Authority (OLP) got two bids, one from Hutchison Port Holdings teaming up with pharmaceutical firm Alapis and one from Cosco Pacific.
The winners of the tenders for Piraeus and Thessaloniki will operate and expand three of their commercial docks for up to 35 years. The companies have not said when the winners will be announced.
Dockers protesting against the government's plans to partly privatise Greece's major ports have refused to work overtime since the start of the year -- causing serious delays in container processing -- as they fear job cuts.
"The completion of the tenders will mean more jobs for port employees. I urge them to return to their normal working hours," Voulgarakis said.