Surfing was proposed as one of five new sports by Japanese organisers last year, along with baseball and softball, karate, skateboarding and sport climbing.
All five were accepted by the International Olympic Committee (IOC) Executive Board last month.
A final decision will be made by the IOC membership-at-large during next week's IOC Session in Rio de Janerio.
Approval for all five is considered a formality.
“With just seven days to go until the IOC decides on whether surfing joins the sports programme for Tokyo 2020, the surfing family is filled with excitement and anticipation about this potentially game-changing moment for our sport," said ISA President Fernando Aguerre.
“Our relationship with the IOC and inclusion in the Olympic Games has been a strategic priority for the ISA for many years and we are thrilled to be on the cusp of realising our Olympic dream.
"I’d like to express our sincere thanks to the IOC and Tokyo 2020 for providing us with this amazing opportunity."
Surfing have run an impressive campaign in recent years, gaining acceptance on the programmes for other sporting events, including the Pan American Games.
It is seen as a sport which would allow the Olympics to embrace a younger population.
Action is expected to take place on natural waves close to Tokyo, with the only lingering concern over whether those waves would be big enough during the Games.
“We are especially excited for the athletes, including budding stars and current elite surfers who would have the chance to represent their nations and showcase their talents on the greatest sporting stage," added Aguerre.
"We head to Rio with gratitude and hope, fully committed to seizing this unique opportunity for all surfers worldwide.”