The "ultimate objective" of Celestyal was new builds, and the line was working with a ship designer to achieve its aim.
"The ultimate objective is to get into new builds but it's a lot of money," Anastassiadis explained. "We are in active discussions about new builds and we are working with a designer in terms of specifications.
"We don't want to get into big vessels, the maximum size we are looking at would be 1,800 passengers and around 60,000 tons."
He added that the ship - or ships, as there would likely be two - would be specially designed for 3-or 4-day itineraries, and all outside cabins would have balconies.
"The problem is the shipyards are full and the earliest we would get a new build would be 2021 or 2022," he added.
The line currently operates three ships - Celestyal Olympia, Celestyal Crystal and Celestyal Nefeli - the youngest of which is 24-years-old. It will take delivery of two more - Thomson Majesty and Thomson Spirit - next November, which date from 1992 and 1983 respectively.
Ahead of any new builds, Mr Anastassiadis confirmed the line would base Celestyal Olympia in the Gulf from November next year. The 1,664-passenger ship will be based in Dubai and offer 3- and 4-night cruises taking in Muscat (Oman), Dohan (Qatar) and Bahrain until April 2018.
"We're adding something new to the Gulf," explained Mr Anastassiadis. "All the other cruise lines operating in the Gulf operate seven-day itineraries, we want to offer something different."
Earlier this year, the line confirmed that Celestyal Crystal would be based in Cuba year-round from this November - and could be joined by a fleetmate from November 2017.
"We haven't finalized how we deploy that vessel [Thomson Spirit] yet. We've got quite a few options, and it's a matter of deciding which one, but one could be we introduce a second vessel in Cuba."
He said that a second ship in Havana would likely offer 3- or 4-day itineraries, in keeping with the line's successful Aegean cruise model.
He added that the 1,462 Thomson Majesty could be deployed in the Western Mediterranean, visiting smaller ports which are currently not served by the larger cruise lines.