PARIS—French state-controlled power utility Eléctricité de France SA is planning to make an offer for the reactor unit of nuclear engineering firm Areva SA, as the government seeks to reorganize France's nuclear sector.

Following requests from Economy Minister Emmanuel Macron, EDF Chief Executive Jean-Bernard Lévy on Tuesday said the company, which operates 58 French reactors, plans to make an offer in the coming days.

Mr. Lévy said an offer would be made at "a fair price, a market price," but he didn't elaborate further.

Areva's management will evaluate the offer, but the government will have the ultimate say, said Philippe Varin, the company's chairman and EDF board member.

"It is the state, as the controlling shareholder of both companies, that must decide on the matter, and it has said it would do so before the summer," Mr. Varin told reporters on the sidelines of EDF's annual shareholders meeting on Tuesday.

The government owns more than 85% of both EDF and Areva.

As Areva plunged deep into the red last year, dogged by an adverse market for nuclear reactors since the Fukushima disaster, poor investment decisions and cost overruns on two projects in France and Finland, Mr. Macron decided to push for a tie-up with EDF.

The French utility operates the world's largest fleet of nuclear reactors and is one of Areva's largest customers.

After posting a €4.8 billion loss in 2014, Areva has embarked in an aggressive cost-cutting effort that includes between 5,000 and 6,000 job cuts.

The initiative from the government is just the latest in a long-standing effort to reorganize France's nuclear sector, which has lost ground against competitors from Russia, South Korea or the U.S.

The government has asked top executives at both companies to make proposals, and will make a decision based on the outlook for the nuclear industry in the long term, said an aide to Mr. Macron.

The valuation of the Areva unit, which represents about 40% of the company's revenue, still has to be determined both Mr. Varin and Mr. Lévy said Tuesday.

Even though Areva owns and operates factories with one of the most advanced technology in the world, its nuclear reactor business, called Areva NP, has posted losses over the past four years.

Analyst Pierre Boucheny at brokerage Kepler Cheuvreux estimates the unit made a negative EBITDA on its reactor construction and servicing business of about €1 billion ($1.11 billion) over the past five years. The nuclear fuel manufacturing has been slightly profitable over the period, he said.

Mr. Boucheny estimates the unit might be worth between €3.5 billion and €4 billion given its outlook and the fact that EDF wouldn't take the liabilities related to the nuclear reactor being built in Finland.

French utility Engie, formerly known as GDF Suez, also has said that parts of Areva looked attractive and could take part in the process. The utility is also an Areva customer.

Mr. Varin said Areva is talking with other potential partners.

He said the solution must make industrial sense and allow Areva to remain a "robust actor" in the industry.

Areva is holding on Thursday its annual shareholders meeting, and on June 3 President François Hollande is expected to meet with Mr. Macron and other officials to discuss the Areva situation.

Write to Inti Landauro at inti.landauro@wsj.com and Nadya Masidlover at nadya.masidlover@wsj.com

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