The mining company's stock spiked 28 percent during the regular session, before Icahn's 8.5 percent stake became public. It added 20 percent in extended trading.
Freeport-McMoran's performance has suffered amid a prolonged drop in commodities prices, including an 18 percent dip in copper this year. On Thursday, the company said it would cut its 2016 capital expenditure estimate by 25 percent, or $700 million, as part of a previously announced review of operations.
Icahn could address capital expenditure and executive pay practices with the company's management, Dow Jones reported. The report said he would also look to trim high-cost production.
Freeport-McMoRan last month posted a net loss of $4.16 per share for the first six months of the year. The shares have skidded more than 50 percent this year.
Icahn could seek representation on the company's board but had not talked to leadership as of Wednesday, according to the wire service.
"FCX maintains an open dialogue with our shareholders and welcomes constructive input toward our common goal of enhancing shareholder value," Freeport-McMoRan said in a statement.
Correction: An earlier headline misidentified the size of Carl Icahn's stake. He owns 88 million shares of Freeport-McMoRan.