It is among four sports that organisers will propose to the International Olympic Committee (IOC), as well as surfing, climbing and skateboarding, which will all debut at Tokyo 2020.
Squash campaigned unsuccessfully for inclusion in the Paris Games, as did billiard sports and chess.
Breakdancing was included in the Youth Olympic Games in Buenos Aires in 2018.
The IOC will consider the proposal and must reach a decision by December 2020.
Tony Estanguet, a three-time canoeing Olympic champion and head of the Paris 2024 organising committee, said the inclusion of the new sports would make the Olympics "more urban" and "more artistic".
Russia's Sergei Chernyshev, competing under the nickname Bumblebee, won the first breakdancing - known as 'breaking' - gold medal for boys at last year's Youth Olympics, while Japan's Ramu Kawai won the girls' title.
The Youth Olympics saw competitors involved in head-to-head "battles" and it is reported that this format would be used in Paris.
Team GB had no breaking competitors in Buenos Aires.
A Team GB spokesperson said: "We look forward to welcoming all new sports into the Olympic Games and will work with the relevant bodies to develop our relationships at the appropriate time.
"Although we did not compete in what was an invitational event at the recent Youth Olympic Games in Buenos Aires, we did witness the popularity of breakdancing among fans there."
As well as the proposed sports, Paris organisers also announced that the 2024 Games would allow the public to immerse themselves in the Olympic experience, through virtual and connected sports.
In addition, members of the public will be able to run the marathon course on the same day as the event - straight after the Olympic race - under the same conditions as those faced by the athletes.
"With Paris 2024, the spectators of the Games finally become actors of the Games," said Estanguet.
Squash's failure to make the list of proposed sports was met with "great disappointment" by the sport's governing bodies.
In a joint statement, the World Squash Federation (WSF) and the Professional Squash Association (PSA) said: "We truly believe squash could seamlessly integrate into the Olympic programme with minimal costs and an optimised pool of participants.
"Our unique interactive glass court would allow squash to bring a lot of additional excitement and spectacular action to any iconic monument of the host city or shed a new light on less known urban areas, while also helping to engage young people in the sport from day one of the preparations and well beyond the Olympic Games."
Karate will make its Olympic debut at the 2020 Games but has not been included on the shortlist of proposed sports for the Paris Games four years later, with the World Karate Federation (WKF) saying it was "deeply saddened".
"Our sport has grown exponentially over the last years, and we still haven't had the chance to prove our value as an Olympic sport since we will be making our debut as an Olympic discipline in Tokyo 2020," said WKF president Antonio Espinos.
"Over the last months, we have worked relentlessly, together with the French Federation, to achieve our goal of being included in Paris 2024.
"We believed that we had met all the requirements and that we had the perfect conditions to be added to the sports programme; however, we have learned today that our dream will not be coming true."