Paris mayor Anne Hidalgo said she hopes the Olympic flame suspended below its balloon can remain in central Paris near the Louvre museum after the games end.
The flame - which is not a flame but an illusion of fire created with lights - has become a fixture of the Paris Olympics, with hundreds of Parisians and tourists coming to watch it every evening when it goes up at sundown in the Jardin des Tuileries park near the Louvre.
Hidalgo said it was not her decision to make, as the Louvre and Tuileries are state property, but added she had written to President Emmanuel Macron, asking for the flame to remain in place and not be moved to another location.
"I would very much like to keep this symbol of the games at this very spot because elsewhere it would not have the same significance," Hidalgo said in an interview with France 2 television on Wednesday.
"Our heritage has been magnified by these games, and I think we need to add to it. Everybody is in love with Paris today, so let's continue," she said.
The designer of France's Olympic cauldron, Mathieu Lehanneur, has said it would be an honour if the attraction were to become a permanent feature of the Paris skyline, much like the Eiffel Tower did after the 1889 World Fair.
Every day since the games opened, thousands have booked free tickets to get a close-up view of the cauldron in the daytime, before it rises above the French capital suspended below a hot-air balloon.
The balloon and its cauldron were unveiled on July 26, when French three-time Olympic gold medalists Marie-Jose Perec and Teddy Riner lit the flame at the end of the opening ceremony.
The Eiffel Tower, Paris' best-known landmark, was built for the 1889 World Fair and meant to be destroyed. That never happened.
For now, the flame is set to be dismantled after the Olympic and Paralympic Games are over. Some have suggested it be moved to Parc de la Villette in northeast Paris, where several countries including host nation France have built national centres for their delegations.
French state-owned electric utility EDF, which is in charge of the flame, has said the flame is based on the simultaneous and controlled projection of a spray of mist and a powerful beam of light.