Squash, snooker and billiards are the latest to push their case to be added to the Tokyo sports program.
The International Olympic Committee passed a resolution in December that allows Tokyo organizers to request the addition of one or more new sports.
Baseball and softball, which were dropped after the 2008 Beijing Games, are considered favourites for inclusion in Tokyo. Several other sports, including karate and wushu, are also lobbying for a spot.
The head of the World Squash Federation, N. Ramachandran, made his case in meetings with Tokyo organizing committee chairman Yoshiro Mori in Tokyo. The squash leader also met with Japanese IOC member Tsunekazu Takeda.
"I was grateful to highlight how serious WSF is in its efforts for squash to be included in the Olympics as a medal sport," Ramachandran said.
Squash was unsuccessful in previous bids for inclusion in the 2012, 2016 and 2020 Olympics.
The World Professional Billiards and Snooker Association and the World Confederation of Billiards submitted a joint bid to win a spot in Tokyo.
The sports previously planned to seek inclusion in the 2024 Olympics, but decided to push for 2020 after the IOC opened the door for Tokyo.
"Snooker has grown at unprecedented levels in recent times and it has been our belief for some time that we should be given our chance on the ultimate global platform for sport," WPBSA chairman Jason Ferguson said.