AMC Entertainment Holdings Inc. is nearing a restructuring deal that would help stave off a near-term bankruptcy filing while turning down a competing financing offer from senior lenders including Apollo Global Management Inc., according to people familiar with the matter.

The proposed deal, which could be announced within days, would require bondholders to provide a $200 million senior loan and to swap their unsecured claims at a discount for new, second-lien debt, people familiar with the matter said. Private-equity firm…

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