Nelson Peltz calls on Pepsi to buy Mondelez

David A. Grogan | CNBC

Nelson Peltz

Trian Fund Management's Nelson Peltz said Wednesday that Pepsi should acquire the snack maker Mondelez at the Delivering Alpha conference presented by CNBC and Institutional Investor.

Trian is a big shareholder of both companies. As of March 31, Trian owned 12 million shares of Pepsi and 40 million shares of Mondelez, which is the snack food company spun off from Kraft last year, according to regulatory filings.

Peltz said Pepsi should buy Mondelez and then spin off the soft drink business altogether. He argued that consumer tastes are turning against soft drinks.

Peltz also said that if Pepsi doesn't want to acquire Mondelez, it should spin off its Frito Lay unit.

(Read more: Midday movers: DD, PEP, CAT & more)

Peltz, who said that Trian is releasing a white paper on the plan for a merger of Pepsi and Mondelez, is well-known as an activist investor, although he prefers to privately negotiate with companies rather than challenge them publicly. He has played a role in some of the biggest deals in the food sector and often urges companies he invests in to spin off businesses and merge with others.

He said that Trian would be meeting with Pepsi's management to discuss the proposal "in the very near future."

Following the disclosure of Trian's stake in the company this past spring, Pepsi said it had held talks with the hedge fund to "consider their ideas." Trian and Pepsi reportedly agreed to keep these discussions private. This is the first time Trian has publicly revealed its plan for the company.

At one point during his session, Peltz got big laughs when he joked that Mondelez was an awful name. "It sounds like a disease," he said. "I am suffering from Mondelez."

Peltz also revealed at Delivering Alpha that he had amassed a large stake in DuPont.

—By CNBC's John Carney. Follow him on Twitter @carney.