Financial Times says those cuts would hurt food companies like Kraft that rely on food stamp recipients buying snacks and drinks.
Tony Vernon, who becomes chief executive of Kraft in October, said that at least one-sixth of Kraft's revenues comes from food stamp purchases and that the portion of sales through the programme was probably larger.
"Our biggest challenge is feeding the 50m Americans who live below the poverty line," Mr Vernon said. "I personally think that it is so important to feeding America's families, and I hope that it [Snap] continues."
Food companies have fought against legislation that would limit purchases of sugary soft drinks and unhealthy food with food stamps. Fast-food restaurants have been trying to get benefits from the programme.
Last year, Yum Brands, the operator of KFC, Taco Bell and Pizza Hut, drew criticism when it tried to convince lawmakers in several states to allow its restaurants to accept food stamps.
"While much attention has focused on how farm subsidies fuel our cheap, unhealthy food supply, Snap represents the largest, most overlooked corporate subsidy in the farm bill," Michele Simon, president of Eat Drink Politics, an industry watchdog group, wrote in a recent report.