The company is building on an animal welfare programme already introduced to meet consumer demand for healthy food.
The Wall Street Journal quotes one of the company's representatives saying that Safeway is "actively looking" to increase the amount of poultry it buys from producers that use "controlled-atmosphere stunning".
This method gases birds rather than using electricity and a mechanical blade.
Safeway also hopes to increase the quantity of cage-free eggs sold to at least 6 per cent by 2010 and increase the amount of pig meat it purchases from suppliers that don't use gestation crates (metal enclosures that confine pregnant pigs) by 5 per cent over each of the next three years.
Brian Dowling, Safeway's vice president of external affairs, stressed that these changes will not mean higher prices for customers, partly because the company is introducing them in a "careful, thoughtful way".
These moves have led to praise from the Humane Society and PETA (People for the Ethical Treatment of Animals), two organisations that have not always been so positive about the company.
Paul Shapiro, a senior director at the Humane Society said: "Safeway's move send(s) a strong message to the agribusiness industry that it must rapidly move away from the worst factory farming abuses, such as intensive confinement systems and the conventional poultry slaughter method."
On its website Safeway promotes itself a "retail industry leader in animal welfare", saying that it understands its responsibility to work with suppliers to ensure that animals in the food production system are treated humanely.
The company says that its animal welfare programme requires that meat, pork, poultry, dairy and seafood suppliers meet a set of designated animal treatment guidelines, and Safeway-brand processors also have to demonstrate that they require their raw material suppliers to meet these standards.
Safeway conducts an audit programme to ensure standards are met, the results of which are reviewed by the company's Animal Welfare Council, the company said.
Safeway has 1,743 stores in the US and Canada