REUTERS/Eduardo Munoz
According to the Journal, Ackman has amassed a 7.5% stake in the company when options contracts are included, and this stake could be revealed as soon as Thursday morning.
Ackman runs the $20 billion hedge fund Pershing Square.
The Journal notes that were Ackman to push for a sale of Mondelez, its market cap of over $70 billion likely provides few suitors.
Among companies floated by the Journal, however, are Kraft Heinz, which recently completed a merger and is owned by 3G Capital and Warren Buffett's Berkshire Hathaway.
Ackman invests with 3G, but the Journal reports that he did not discuss this position with 3G ahead of time.
As Business Insider's Julia La Roche reported back in June, Ackman said earlier this year that Pershing Square had made two new investments: one large and one small.
A Forbes report said that Ackman had taken a stake in Nomad Holdings, a special-purpose acquisition company that trades on the London Stock Exchange. Pershing's stake in Nomad was worth around $350 million, almost definitely making it the smaller of Pershing's two new investments.
And now it appears this Mondelez stake is the big one.