Two Super League club presidents are already among 10 people arrested in the last 48 hours in connection with the case, with the authorities announcing the identities of another 70 people against whom charges have been filed.
Marinakis, who took over the presidency of Olympiakos in July 2010 and was appointed Super League chief in August 2010, is accused of being involved in "simple collaboration with a criminal organisation whose members seek financial or other material benefit", and "simple collaboration in corruption, altering the results [outcome] of matches.
Olympiakos issued a statement saying: "Concerning the suspicious games it should be noted that all relate to the 2008/09 and 2009/10 seasons except one and Olympiakos are not involved in any of these games. Also, Mr Marinakis was not president of Olympiakos at the time."
"Secondly, in terms of what is said in the [recorded] dialogues, there is no evidence of any crime, and thirdly we must stress that Olympiakos monitor developments but our priority is to build the team ahead of next season."
Papadopoulos, who plays for champions Olympiakos, was also included in the list along with another high profile player, Kostas Mendrinos, who is on the books of Aris Salonika.
The pair have been charged with breaching the "regulations of OPAP (the state-owned betting company) and other provisions."
Greece Under-21 coach Giorgos Georgiadis, a former Greece international, has also been identified and faces the same category of accusations as Papadopoulos and Mendrinos.
The Hellenic Football Federation (EPO) was not immediately available for comment with its general assembly in progress.
ROCK BOTTOM
Achilleas Beos of Olympiakos Volos and Kavala's Stavros Psomiadis were arrested along with seven others on Wednesday on charges of betting fraud before the authorities announced a list of 15 people in total in a scandal dubbed "Koriopolis" by local media.
In a further twist, Psomiadis's father Makis - a former president of Kavala and AEK Athens - is among the people police are searching for.
Legal proceedings are expected to begin on Monday.
The Greek government responded to the arrests by pledging to get to the bottom of match-fixing allegations as part of a wider effort to tackle corruption in the debt-ridden country.
"This investigation is an opportunity to recover from what is the darkest page in the history of Greek football," Deputy Culture Minister Giorgos Nikitiadis said on Thursday.
"It will go as deep and as high as necessary. Our basic target now is to clean up the sport and give the people back the game."
The Super League declined to comment with the investigation continuing but AEK Athens president Stavros Adamidis said the domestic game had reached "rock bottom."
