Metro, Lidl and Kik are thinking about signing a fire protection agreement with the international organisation the Clean Clothes Campaign, the taz newspaper said in a report due to be published on Monday.
American firm PVH, which owns the Hilfiger and Calvin Klein brands, as well as Tchibo have signed up to the agreement, which requires three more large companies to sign to take effect.
Budget clothes retailer Kik in October earmarked more than $1 million for victims of a fire in a Pakistani factory where nearly 300 people died while making jeans for the high street chain.
"We are currently conducted inquiries among all our 120 suppliers to try to identify which gaps there are in fire safety," Kik manager Michael Arretz told Focus news magazine.
More than 350 people have died in recent clothes factory fires in Karachi, Pakistan and Dhaka, Bangladesh, highlighting the often terrible conditions in which cheap clothing is made.
Arretz told the Welt am Sonntag weekly newspaper that higher prices did not necessarily guarantee a clean conscience for shoppers though. He said large and expensive brands "often manufacture in the same Bangladeshi factories as us."