Kraft shares jumped more than 14 percent on the news. See what the stock is doing now.
The Brazilian firm has some $5 billion burning a hole in its pocket and has been searching for acquisition deals, according to the Journal.
It was not immediately clear whether 3G's bid would involve Warren Buffett, who partnered with the firm on both its Heinz and Tim Hortons deals in recent years.
Buffett's Berkshire Hathaway held nearly 193,000 Kraft shares as of the firm's most recent SEC filing.
Berkshire sharply decreased its stake in Kraft in 2013. At one point, before its split into Kraft and Mondelez, he was the largest shareholder in the former company.