A source at Greece's Hellenic Football Federation confirmed to AFP in Athens that the three countries were holding discussions about a joint bid to host the 2030 World Cup.
If successful, the event would be held in the northern winter to avoid extreme temperatures in the three countries, as with this year's World Cup in Qatar, British newspaper The Times reported on Thursday.
"The three countries are working flat out" and "the application to organize (the 2030 World Cup) is being studied", sports ministry spokesman Mohammed Fawzi told DMC television.
"Egypt will be one of the best countries" to organize such a sports event, he said, stressing that his country had hosted many world championships in the past three years.
The bid by Egypt, Greece and Saudi Arabia will come up against at least two other joint proposals.
Argentina, Chile, Paraguay and Uruguay launched a bid to host the 2030 World Cup in early August, while Spain and Portugal announced their joint candidacy last year.
The joint South American bid aims to stage the 2030 final in the very same Centenario stadium in Montevideo that hosted the first title match 100 years earlier.
World football's governing body FIFA is due to select a host for the 2030 tournament in 2024.