Industry Minister Arnaud Montebourg told lawmakers that the interested party was a private investor from the steel industry who wanted to inject money into the site with the financial backing of the French state.
France has raised the prospect of the site being taken temporarily into state hands if no sale agreement is reached.
"(The party) "is ready to invest nearly 400 million euros to renovate this site," Montebourg told parliament, without giving the potential buyer's identity.
Montebourg said the aim was for the operation to have a zero cost for public finances and the government was mulling using existing state stakes in companies to fund any Florange deal.
On Tuesday, President Francois Hollande pressed ArcelorMittal CEO Lakshmi Mittal to keep two threatened blast furnaces running or agree to sell the whole site, raising the possibility of a temporary state takeover while the government looks for a permanent buyer.
ArcelorMittal has so far said that it wants to sell only the idled furnaces and not the entire site, a steelworks near the German border that employs some 600 people.
The company has told France's Socialist government that it plans to shut down the furnaces, which it says are no longer economically viable, unless a buyer willing to take them over can be identified by a December 1 deadline.
Steel industry experts say it would be tough to find a buyer for the furnaces alone without the adjacent steel plant.
Earlier, Finance Minister Pierre Moscovici said the prospect of a temporary nationalisation of Florange was a special case and did not meant that further state takeovers for threatened factories were being prepared.
Copyright @ Thomson Reuters 2012