Mayor Anne Hidalgo said she would like to see some of the swimming events staged in the Seine, and for parts of the river opened up for public use.
"I want swimming in the Seine to be made possible by 2024," she said, adding that preparations for the Olympic bid presented a "historic opportunity" to improve environmental protections, transport and accommodation in the city.
Hidalgo said she hoped to see the swimming stage of the triathlon and the 10-kilometre open water event staged in the Seine.
The quality of the capital's famed waterway has improved in recent years, but sewage pipes still spew 2.5 million cubic metres of waste every year into the river, which is also polluted by effluents from factories upstream.
Hidalgo's ambition comes nearly three decades after mayor Jacques Chirac -- who later became president -- vowed in 1988 to swim in the Seine five years later, which he famously never did.
Paris faces competition from Los Angeles, Rome and Budapest to host the 2024 Olympics.
The winner will be named on September 13th, 2017, in Lima.
In Paris, locals have shown that if the weather gets hot enough then the murky waters of the city's waterways hold no fear.
Some brave or foolhardy locals, depending on your point of view, found a radical way to stave off a heatwave last year - by jumping into the city's canals.
Indeed, the Bassin De La Villette, which links the Canal St Martin and Canal de l'Ourcq in the 19th arrondissement, appeared to be the city's newest spot for a dip.
The video below from Le Bonbon website shows bathers plunging into the water from the bridge and leisurely drinking a beer or two in inflated floats.