Work slowdowns may also be staged as part of the anticipated labour unrest.
The move to lease the two container ports to private operators had been attempted a year ago leading to an entire month of repeated strikes and slowdowns, said shipping weekly Fairplay.
Relations have reportedly been 'tense' with both sides sticking to 'uncompromising' views about the terminals' future.
Greek union leaders have constantly threatened labour unrest in response to privatization drives.
This new round of potential strikes have been triggered by Wednesday's announcement by the new Greek Shipping Minister Giorgos Voulgarakis that a global tender for operators to run Piraeus and Thessaloniki under a 30-year concession would be launched in the first half of January.
The port unions proceeded to announce action that will be decided in the following week.
Piraeus and other Greek ports had already suffered a 24-hour strike last Wednesday which disrupted all normal port operations and slowed down bunkering.