The potential move is being studied by officials working for Arnaud Montebourg, the Industrial Recovery minister, just 10 days after the government rejected a similar proposal for ArcelorMittal's Florange steel plant in eastern France, the daily said.
Montebourg was vociferous in his support for nationalisation in that case and was reported to have come close to resigning after failing to convince his colleagues in a debate that exposed fault-lines within the Socialist government.
The minister's officials are currently negotiating with Rio Tinto's Rio Tinto Alcan unit over the future of the plant at Saint-Jean-de-Maurienne in the French Alps.
Key to the negotiations is the company's demand for a reduction in the prices it pays for electricity bought from energy giant Electricité de France (EDF), in which the government has a controlling stake.
The plant's current electricity deal expires in the spring of 2014 and Rio Tinto has threatened to sell or close it if its demands are not met.
In October, it said several potential buyers had been in touch about a possible takeover.
Like Florange, the aluminium plant is seen as a symbol of France's declining industrial base.
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It was originally owned by French group Pechiney, which was bought out by Canada's Alcan in 2003. Alcan itself was taken over by Rio Tinto four years later.
There was no immediate comment on Le Monde's report from either the government or Rio Tinto.