"There are discussions underway at the request of the Saudis," said the defence ministry, which owns the building and its grounds.
"There are strict conditions that the Saudis have not yet accepted," a statement from the ministry added.
Many countries erect temporary pavilions during the Olympics which are used for national promotion as well as spaces for fans and official events.
Right-wing MP Nathalie Serre raised the issue in parliament on Wednesday, calling the Invalides "an architectural treasure, full of symbolism and the history of our country" and reminding MPs that the building also contained a military hospital.
"Saudi Arabia poses a specific problem because of its human rights record, but even if it was a Danish or Canadian village it would be the same issue," she told AFP on Thursday.
"There are some things that are not for sale or for money-making, and the Invalides in my opinion is one of them."
The defence ministry said that any funds raised from the project would go towards the army museum and hospital inside the Invalides, whose golden dome is one of the boldest features of the Paris skyline.
Napoleon's remains were buried there in 1861, forty years after his death on the remote Saint Helena island in the middle of the South Atlantic.
The monument is already used as a backdrop for fashion shows, but Serre said it was different to rent it out to a foreign state.
Responding to her question in parliament, Veterans Minister Patricia Miralles stressed that "nothing is confirmed, nothing has been done".
The Paris Olympics take place from July 26-August 11 followed by the Paralympics from August 28-September 8.
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