Talks are continuing with Campbell and at least one other potential suitor, one of the sources said on Thursday.
The sources, who cautioned there may be no deal, requested anonymity because the information is confidential. Snyder's did not immediately respond to requests for comment; Campbell declined to comment.
The approach underscores the drive for food industry consolidation as traditional food companies watch their sales drop and struggle to create growth or innovation on their own. Meanwhile, scale is increasingly important to bargain with grocery stores and retailers who are under their own pressure as shopping shifts online.
Snyder's-Lance has a market capitalization of $3.82 billion, while Campbell has a market capitalization of $14.65 billion.
An acquisition of Snyder's would be one of the company's boldest moves, as Campbell CEO Denise Morrison heads into her seventh year in the job.
It would bring with it snack brands that complement Campbell's Pepperidge Farm business, as its core soup offerings remain out of favor.
Snyder's-Lance, owner of brands like Cape Cod potato chips, Snyder's pretzels and Pop Secret popcorn, was put together through a compilation of deals. Snyder's merged with Lance in 2010. The combined company bought Diamond Foods in 2016.
It has struggled recently though with operational challenges, including a more costly than expected integration of its Diamond acquisition. Pop Secret has come under pressure as consumers shift from microwavable popcorn to newer, fresh-popped brands like Angie's Boomchickapop.
Earlier this year, Snyder's CEO Carl E. Lee, Jr. stepped down from the role after working at the company for 12 years. He was replaced by Brian Driscoll, former president and chief executive of Diamond Foods.
Campbell has for years looked to acquisitions to help diversify away from its reliance on packaged foods, as consumer tastes have moved to fresher alternatives. It acquired dressing, beverage and vegetable company Bolthouse Farms in 2012 for $1.55 billion. This month it completed its $700 million acquisition of organic broth and soup company Pacific Foods.