The government wants to pass laws punishing violence at sports events, including imposing fines and threatening to cancel matches. Football's governing bodies have strict rules protecting their member federations' independence to run their own affairs.
UEFA general secretary Gianni Infantino says a joint letter with FIFA was sent to the Greek government on Wednesday. Infantino hopes the threat "will make them reconsider their actions, so we can still work together to resolve the issues affecting Greek football."
Teams and officials from suspended countries cannot take part in international matches and meetings. In 2006, FIFA briefly suspended Greece, then European champion for government interference.
The new bill introduced by Sports minister Stavros Kondonis has caused controversy in Greece too. Most football clubs, including those crying out about football governing corruption for years, are opposing it, while most football fans are supporting it.
Corruption in Greek football has become commonplace in the past 20 years, with many cases coming before the Greek courts, but being dismissed on technicalities, or backing down of essential witnesses.
A massive corruption case based on evidence provided by years of phone tapping by the Greek security services has just been kicked off in court. At least a few years are expected before a final verdict is out.
In the past 20 years, one club -Olympiacos Piraeus- has celebrated 18 championship titles, with pundits and football fans speculating the club has some involvement in match fixing and wider corruption.