Rehhagel's contract expires on June 30 and his assistant Yiannis Topalidis, who announced his departure after Tuesday's 2-0 loss to Argentina in their final group game, confirmed the 71-year-old German has bid farewell to his players.
"I have said what I had to say," Topalidis told reporters late on Wednesday before the Greek team boarded their flight home. "I have said goodbye to the players and so has the coach."
Greece's football federation is expected to formally announce Rehhagel's resignation and successor in the next few days following the squad's return from South Africa on Thursday.
Former PAOK Salonika coach Fernando Santos is the early favourite to replace Rehhagel but said he had not yet been contacted about the job despite reports in the Greek media that he had already agreed a two-year deal in principle.
"I have not received any proposal from the Greek football federation (EPO)," the 55-year-old Portuguese told Novasport FM. "At the moment, that has not happened. If such a proposal comes then I will study it seriously."
Santos, who has enjoyed great success as a club coach in the country, was recently named Coach of the Decade at a ceremony in Greece in recognition of his growing influence on Greek football.
The Lisbon native has coached three of Greece's biggest clubs in AEK Athens, Panathinaikos and PAOK, who won the league playoffs last season to finish runners-up.
It was their highest placing for 24 years and secured a place in the Champions League qualifying rounds.
The Greece squad returned to Athens in the early hours of Thursday morning, leaving Rehhagel behind in Durban with the former Bayern Munich coach opting to stay behind to rest and follow the rest of the tournament in South Africa.
Rehhagel has almost completed nine years in charge, guiding Greece to unprecedented success. Ranked 100-1 outsiders, they beat France and hosts Portugal in the final to win Euro 2004.
