None of the potential buyers, which include GFG Alliance and former owner Greybull, would be willing to take on the whole company, even for a nominal sum, because of the capital expenditure required to make it profitable after years of underinvestment, the sources said.

They added that June 12 is the deadline for binding bids for the country's second largest steel producer.

British Steel, which produces high-cost long steel products used in construction and rail networks, was put into compulsory liquidation on May 22, jeopardising 5,000 jobs at the company and a further 20,000 more in the supply chain.

Unions oppose a break up of the business, making any partial sale politically difficult, but the British government is under pressure to find a quick solution as it potentially faces a wage bill of around 250 million pounds a year until a buyer is found, one of the sources said.

GFG Alliance, a privately held conglomerate led by Sanjeev Gupta, is likely to make an offer for operations that have synergies with their existing steel assets in the region and the more profitable ones, a second source said.

GFG, via its Liberty House unit, bought Scunthorpe-based Caparo Merchant Bar, which produces steel bars for construction, energy and infrastructure, from administrators in 2017.

GFG Alliance declined to comment.

Greybull Capital, which paid former owners Tata Steel a token one pound for British Steel three years ago, is interested in buying its operations in France and the Netherlands, which specialise in rail, wire and processing, one of the sources said.

"We will explore all options to help the company find the best sustainable solution for the good of its employees, customers and all involved," Greybull told Reuters in an emailed comment.

British Steel's advisor EY has also reached out to other European steelmakers including Italy's Marcegaglia Group, AFV Beltrame Group and Acciaierie Venete, and also international players such as India's JSW Group and Posco Steel, two of the sources said.

Private equity firm Endless, which was a bidder for the steel assets at the time of the Greybull takeover, could also make a proposal, they said.

Not all of those contacted were likely to bid. Marcegaglia, for instance, will not do so as it does not see synergies with the British producer, a source close to the company said.

Across Europe, the steel industry is struggling with cooling demand and growing supply, in part as steel tariffs deflect supplies from the United States, steelmakers say.

Analysts have said more consolidation of the European steel industry is inevitable.

Gupta's Liberty House Group is already buying assets across Europe after the European Commission approved ArcelorMittal's purchase of Ilva on condition it sold off works in Romania, the Czech Republic, Italy, Belgium, Luxembourg and North Macedonia.

(Reporting by Clara Denina and Barbara Lewis; Additional reporting by Pratima Desai; Editing by Jan Harvey and Kirsten Donovan)

By Clara Denina and Barbara Lewis