The company behind Burger King and Heinz is reported to be in talks to buy Kraft in a deal that could value the US food giant at more than $40bn (£27bn).
Brazilian private equity firm 3G was said to be in "advanced talks", the Wall Street Journal and Financial Times reported.
In 2103, 3G and Warren Buffett's Berkshire Hathaway teamed up to buy ketchup maker H.J. Heinz for $23bn.
Kraft shares jumped 15% in after-market trading following the reports.
Based on Tuesday's closing share price of $61.32, Kraft was worth $36bn. But any buyer would typically have to pay a significant premium over the market value.
Kraft, known for its cheese of the same name and also Philadelphia, is one of America's biggest food companies. It owns Maxwell House coffee and in 2010 bought the UK chocolate maker Cadbury for £11.5bn.
Kraft no longer owns Cadbury after spinning it off in a company called Mondelez, which also includes the Toblerone, Kenco and Oreo brands.
3G was co-founded by Jorge Paulo Lemann, who was a major shareholder in brewer InBev and helped steer its 2008 acquisition of Anheuser-Busch.
The private equity firm has been linked as a bidder for several food groups, and in February was reported to be looking at the Campbell Soup Company.
