The decision to retain squash at this stage was greeted positively by Laura Massaro, the current British Open champion.
"We deserve to be included and it was almost painful to watch London 2012 with no opportunity to be part of the nation's success," said the 29-year-old.
"All of the other notable racket sports are in the Games already - tennis, badminton and table tennis - but squash has been overlooked in the past and it has been tough to take when you compete at the highest level on the world stage."
Ramy Ashour stunning reflex shot
The IOC initially recommended the removal of wrestling after assessing the performance of all 26 sports at the London Games, but it could now be granted a reprieve.
Softball had a presence at the Olympic Games, solely for women, between 1996 and 2008. It was then dropped from the programme for 2012, as was men's baseball, which had appeared sporadically at the Olympics since 1904.
"It has strength, power and, from an energetic sports perspective, it hits all the marks," she told BBC Sport.
Whichever sport succeeds in the September vote will be added to the 25 core sports, plus golf and rugby sevens.
Wrestlers from Russia, the US and Iran form alliance
To remain relevant to sports fans of all generations, the Olympic programme commission systematically reviews every sport following each edition of the Games.
The commission uses 39 criteria in determining a sport's suitability for the Olympic Games, including youth appeal, universality, popularity, good governance, respect for athletes and respect for the Olympic values.
Golf and rugby sevens are the latest sports to be added to the Olympics and will debut at Rio.
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