U.S. Steel has received multiple bids for the steelmaker in excess of $40 a share, sources familiar told CNBC's David Faber Wednesday.
U.S. Steel shares rose more than 3% on the news. The company's stock closed Tuesday at $36.39 a share.
The sale process started in August when rival Cleveland-Cliffs made an unsolicited bid of $7.3 billion. U.S. Steel rejected that offer.
CNBC previously reported U.S. Steel has attracted five bidders, including ArcelorMittal.
U.S. Steel's board is meeting Wednesday, the sources said. The sale process is coming to a conclusion, but this does not mean there will be an announcement of the outcome Thursday morning.
Cleveland-Cliffs' current bid is above $40 a share which is higher than its original offer of $35 a share made last summer, the sources said.
The composition of Cleveland-Cliffs' original bid was $17.50 in cash per share and the rest in stock. The current bid has a similar composition though it may be weighted more toward cash, the sources said.
Cleveland-Cliffs is expected to structure its bid to mitigate the risk of antitrust review. This could potentially include a reverse termination fee or a divestiture package, though nothing is certain.
If Cleveland-Cliffs prevails, its combination with U.S. Steel would account for 40% of flat-rolled steel and 60% of auto-grade steel in the U.S. The combined company would be the 10th-largest steel producer worldwide.
The details of ArcelorMittal's bid are less clear, though the company apparently had financing that would have allowed it to offer $45 a share in all cash.
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