They could reach a deal as early as later on Monday evening, the source said, emphasizing that a final agreement had not yet been reached and that negotiations could still fall apart.
The public battle escalated Friday, with Ackman demanding the ouster of the retailer's chairman, Thomas Engibous, as well as interim CEO Myron Ullman. Ackman demanded that Ullman be replaced within the next 30 to 45 days.
"I have lost confidence in our chairman's ability to oversee this board," Ackman said in a letter last week.
Also on Friday, Starbucks CEO Howard Schultz joined the fray by urging the billionaire's removal from the board.
(Read more: Howard Schultz slams Ackman over JC Penney fight)
On Monday it seemed Ackman might be facing a new foe in his campaign: George Soros.
The chairman of Soros Fund Management, which holds a 7.9 percent stake in the embattled retailer, is reportedly supporting Engibous and Ullman against Ackman's public efforts to replace them, according to Bloomberg.
Another large Penney investor, Glenview Capital Management, also appears to be sitting tight on its "passive" 4 percent stake. A person familiar with the hedge fund, led by Larry Robbins, said it has not taken any sides in the public dispute between Ackman and Penney's board.