The two teams, at the centre of match-fixing investigations, were relegated last month but then exercised their right to appeal and the original decision was overturned.
However, the Professional Sports Committee said on Tuesday that neither club had done enough to break their ties with owners who have been accused of being part of a ring that fixed the outcome of matches.
More than 80 people have been charged with match-fixing while Kavala owner Makis Psomiadis and Volos president Achilleas Beos are banned for life from all soccer activities.
The sports panel also said on Tuesday that Levadiakos and Doxa Drama would be promoted to the top flight in place of the demoted clubs.
A spokesman for the Super League told Reuters: "Officially there has been no postponement of the start of the season but we expect an announcement on Wednesday".
The news of Volos's demotion prompted dozens of fans to protest in the city streets and the local office of the ruling PASOK party was attacked.
The club were due to start the season on Sunday with a fixture at AEK Athens while Kavala were due to open up with a game at Olympiakos Piraeus on Saturday.
Earlier this month UEFA banned Volos from the Europa League and they were replaced by Luxembourg team FC Differdange 03 in last week's play-off round first leg against Paris Saint-Germain.
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