A combination would be the third-biggest takeover in history and the largest acquisition of a UK-based company, according to Thomson Reuters data.
It would bring together some of the world's best known brands, from toothpaste to ice creams, and combine Kraft's strength in the United States with Unilever's in Europe and Asia.
The global packaged food industry is grappling with slowing growth, new competition from upstart brands, deflation in developed markets and more health-conscious consumers.
Although Kraft, which is controlled by U.S. billionaire Warren Buffett and private equity firm 3G Capital, said it looked forward to talking terms, Unilever said it saw no reason to discuss a deal without financial or strategic merit.
Kraft approached Unilever earlier this week, according to people familiar with the matter, who declined to be identified because the approach was confidential.
In its offer, Kraft sought to provide assurances over maintaining its culture of innovation, recognising that this requires investment, and acknowledged that there are limits to cutting costs, one of the people said.
Kraft has also offered to keep three headquarters for the combined company in the United States, Britain and the Netherlands, the source added. Kraft also expects the combined company to be well capitalized, so that its debt is rated investment grade, according to the source.
Kraft has until March 17 to make a final bid for Unilever under UK takeover rules.
Unilever shares rose to a record following news of the offer, which analysts at Jefferies called a "seismic shock", and closed 15 percent higher, short of Kraft's $50 per share offer price, with the news lifting shares across the sector.
Unilever said Kraft's proposal included $30.23 per share in cash, payable in U.S. dollars, and 0.222 of a share in a new enlarged entity per Unilever share and represented an 18 percent premium to its share price on Thursday.
"We believe Kraft will likely need to raise its offer substantially if it hopes to change the outcome," RBC Capital Markets analyst David Palmer said in a research note.
Kraft's move could flush out other bidders for Unilever, but of the potential rivals, U.S. consumer giant Procter & Gamble Co may face anti-trust hurdles, while pharmaceutical and consumer packaged goods company Johnson and Johnson would likely not be interested in household products.
Unilever, which has struggled recently amid slowing growth and currency fluctuations, saw its shares tumble 4.5 percent on Jan. 26, its worst day in nearly a year, when the company reported lower-than-expected fourth-quarter sales. The share plunge encouraged Kraft to make an approach, another source familiar with the matter said, asking not to be named because the matter is confidential.
Unilever has been hit by a slowdown in emerging markets, which it and other consumer companies have long relied on for growth, as well as in its home market, where consumers have been rattled after "Brexit," Britain's decision to leave the European Union last year.
Brexit pushed down the value of the pound, raising the cost of producing consumer goods in Britain and straining relations between the country's retailers and suppliers.
For Kraft, its move comes as low interest rates and cheap debt have fuelled big cross-border deals, making it the busiest start to the year for M&A activity on record.
Still, investors will look at Kraft-Heinz's own track record of boosting sales when evaluating whether they can help Unilever cope with its own slowed growth. Kraft's sales fell 3.8 percent to $6.86 billion in the fourth quarter ending Dec. 31, and its U.S. sales, which account for more than 70 percent of total sales, fell 3.1 percent to $4.84 billion.
Kraft Heinz shares rose more than 10 percent in New York trading, helping lift the Nasdaq to a record high.
3G READY TO DEAL
Although Kraft is smaller than Unilever, with a market value of $106 billion as of Thursday, it is 50.9-percent owned by Buffett's Berkshire Hathaway Inc and 3G Capital, which also controls Anheuser-Busch InBev.
3G, known for driving profits through aggressive cost cutting, has orchestrated a string of big deals rocking the food and drink industry, including Anheuser-Busch InBev's takeover of SABMiller and the combination of Kraft and Heinz.
A deal would offer opportunities to combine marketing, manufacturing and distribution in addition to cutting costs, but some industry analysts said Kraft might not want Unilever's household and personal goods brands and could spin them off.
"This is cheap money meeting industrial logic," said Steve Clayton, manager of the HL Select UK Shares fund at Hargreaves Lansdown, which owns Unilever shares.
"Kraft Heinz are attempting a massive push on the fast forward button ... To acquire the sheer scale of brands that Unilever represents through one-off acquisitions could take decades," Clayton added.
Britain's largest union, Unite, represents employees at Unilever, according to its website. Unite urged Unilever to continue fending off the takeover attempt to prevent job losses.
Unilever employs 168,000 people and generates roughly 17 percent of its revenue in the United States compared with Kraft-Heinz, which generates roughly 78 percent in America.
A recent wave of cross-border deals in Europe is leaving British businesses vulnerable to possible job cuts. Pegeuot SA's proposed acquisition of General Motors Co's Opel business may eventually lead to heavy restructuring at the Vauxhall brands, which employ 4,500 people in Britain, sources said.
Centerview and Morgan Stanley are working with Unilever alongside UBS and Deutsche Bank, who are also acting as corporate brokers. Kraft is working with Lazard.
(Additional reporting by Angelika Gruber in Zurich, Danilo Masoni and Simon Jessop in London and Lauren Hirsch and Greg Roumeliotis in New York)
By Martinne Geller and Pamela Barbaglia