Rome, Paris, Los Angeles and Budapest are bidding to host the Games and, under new regulations, the local organising committee has the opportunity to add five sports to the schedule at its own discretion.
"If Rome hosts the Olympics, cricket will be included," Simone Gambino, president of the Federazione Cricket Italiana (FCI), told ESPNcricinfo.
"We have had a firm commitment from the organising committee."
Earlier this year, the IOC opened up the opportunity for the host city to suggest sports for admission to the program.
The 2020 Olympics, to be held in Tokyo, recently nominated karate, skateboarding, sports climbing, surfing and baseball/softball for inclusion.
Future Games would not necessarily have to include the same five sports which had been selected by the previous host city.
Cricket has not been played at the Olympics since 1900.
The announcement of the host city for 2024 is set to be made in September next year.
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