Activist investor William Ackman has built up a $5.5 billion investment in snack food giant Mondelez International Inc, gambling that the company will become a takeover target as a wave of consolidations sweeps the food industry.

Ackman's latest acquisition, which was first reported by the Wall Street Journal, could raise his total stake -- which includes shares and options -- to 7.5 percent of Mondelez, which has a market capital of $75.6 billion. Ackman believes that the company has to grow revenues faster and cut costs significantly, or sell itself to a rival, people familiar with the matter told the paper.

Sources told CNBC that Ackman's $20 billion hedge fund, Pershing Square Capital Management, was considering a possible takeover of Mondelez.

"We welcome Pershing Square as investors in our company," a Mondelez spokesperson told the Journal. "We'll continue to focus on executing our strategy and on delivering value for all our shareholders."

The Journal speculated that other potential buyers would include Kraft Heinz Co. and PepsiCo Inc. Pershing Square is investing in Mondelez after the company defused a shareholder fight last year, when activist Nelson Peltz joined its board and agreed to abandon a push for a merger with PepsiCo, Bloomberg reported.

The New York Times reported that having two activist investors, Ackman and Peltz, on the company's board could lead to conflict, but cited comments from Ackman made earlier this year in which he said he would be happy to work with Peltz.

“If I ran a company, I would be delighted to have Nelson on my board,” the paper quoted Ackman as saying. “I really mean that. I think it’s very, very helpful to a C.E.O. to have a major shareholder on the board, so that you can get input from a shareholder before you -- you can test something internally.”