The move comes at a sensitive time for the two U.S. food and drink makers. Mondelez, which makes Oreo cookies and Cadbury chocolates, has stumbled in its first quarters as an independent company after splitting from Kraft Foods.
PepsiCo Inc., meanwhile, is reviewing restructuring options for its underperforming North American beverage business. It also owns Frito-Lay, Tropicana and Quaker Oats.
PepsiCo said in a statement that it has held meetings with Peltz's Trian Fund Management in recent weeks to consider its "ideas and initiatives" for long-term growth.
A representative for Mondelez International Inc. wasn't immediately available for comment.