The executive committee of the International Olympic Council (IOC) shortlisted wrestling with squash and baseball-soft ball for the 2020 Olympics.
Only one of these sports will be allowed to participate in the Games in Sochi. The executive committee will meet again later this year in September to take a final call on the matter.
In February, the IOC voted to drop wrestling after the 2016 Rio Games - even though the participation of the sport dates back to the ancient Olympics in 708 BC.
In the meeting on Wednesday night, the other five sports - wushu, rock climbing, wakeboarding, karate and roller sports - failed to make the cut.
The criticism against wrestling is that the sport has failed to modernise, has complex rules and allows little room for participation by women. However, Bill Scherr, the 1988 bronze medallist wrestler from the US and chairman of the Committee to Preserve Olympic Wrestling, told The New York Times that the sport's apex body has taken steps to modernise the game.