The players will return to their homeland this week after they were knocked out of the tournament in Brazil following a last-16 defeat to Costa Rica on penalties.
Instead of receiving extra money for their efforts in the tournament, the players have requested that a new training centre is built in order to develop the national team.
According to news bomb.gr, the letter read: "We do not want as extra bonus, or money. We only play for Greece and its people. All we want is for you to support our effort to find a land and create a sports centre that will house our National team."
The letter was signed by all 23 squad players after it was written yesterday.