UEFA president Aleksander Ceferin and FIFA vice president Greg Clarke "are expected to contribute to the consolidation of the framework so that we can reshape Greek football," government spokesman Stelios Petsas said.
Prime Minister Kyriakos Mitsotakis' government has been drawn into a dispute between two of the country's top clubs, PAOK Thessaloniki and Olympiakos Piraeus.
The Greek professional sports commission had previously recommended the relegation of current Super League champions PAOK over allegations of common ownership of fellow top-flight club Xanthi.
PAOK chief Ivan Savvidis was accused by Olympiakos of acquiring a stake in Xanthi through a family member, a claim which he denies.
The Thessaloniki club have called the accusations a "setup" engineered by arch-rivals and current league leaders Olympiakos.