The private equity firm would pay between $21 and $22 per share in a deal that would likely be announced this week, the report said, citing people familiar with the matter.
The deal would represent a premium of 10 percent or more as the shares were recently trading just above $19, according to the report.
Arconic shares rose almost 4 percent, while Apollo shares were up 2 percent on Tuesday.
Reuters had reported in October that Apollo Global was in advanced negotiations to acquire Arconic.
Elliott Management Corp, the activist hedge fund that sits on Arconic board, is working to address potential liabilities weighing on the sale process for the U.S. aluminum products maker, Reuters had reported in November.
Arconic declined to comment, while Apollo Global did not immediately respond to a Reuters request for comment.
Reporting by Sanjana Shivdas in Bengaluru; Editing by James Emmanuel