The list of additions is due to be revealed by the local organising committee (OCOG) on Thursday and must be signed off on by the International Olympic Committee.
Their inclusion would come on top of the 28 sports already on the programme, although the Paris 2024 committee did not confirm the reports to AFP.
Breakdancing, an acrobatic style of street dance typically set to hip-hop or funk music, would be making its first appearance in the Olympics, while the three other sports will all be introduced at the 2020 Games in Tokyo.
Karate and baseball/softball, all part of the Tokyo programme, are also candidates, as well as squash, which has been repeatedly rebuffed, and petanque.
At least 20 disciplines from federations recognised by the IOC have applied for inclusion.
Local organisers must submit the recommended list to the IOC which will make a decision in December 2020, following the Tokyo Games.
Breakdancing appeared at last year's Summer Youth Olympic Games in Buenos Aires, in the form of "battles" -- or duels -- decided by judges, and falls under the auspices of the World Dance Sport Federations (WDSF).
The IOC and OCOG have already said the number of participating athletes will be capped at 10,500, a reduction from the Tokyo maximum, for the 2024 Games, limiting the hopes of team sports.
Local organisers also suggested the need for the construction of new permanent venues would likely count against sports pushing to be included.
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