Based on the information published by members of the group, the bill would require online platforms to vet sellers to make sure they're legit. The company will also have to remove counterfeit listings and their sellers, as well as be more proactive in preventing continued sale of counterfeits by third-party sellers.

As The New York Times notes, the Department of Homeland Security published a report earlier this year, urging companies to establish stronger policies to protect buyers from fake goods coming from sellers overseas. Peter Navarro, the White House Office of Trade and Manufacturing Policy director who helped oversee Homeland Security's recommendations, criticized Amazon for profiting off counterfeits. "Under current lax interpretations of the law," he said, "e-commerce platforms face virtually no liability for their counterfeit trafficking."

Jerrold Nadler (D-NY), one of the lawmakers who introduced the bill, said in a statement:

"American consumers increasingly turn to the internet to shop. Counterfeiters have followed consumers, and it is clear more must be done to combat the rising trend in online sales of counterfeit products. Consumers should be able to trust that what they see and purchase online is what they will get, but counterfeiters continue to join platforms with ease and masquerade as reliable sellers in order to infect American households with dangerous and unsafe counterfeit products. The SHOP SAFE Act proposes a set of commonsense measures to tackle the gaps in these platforms' systems and stop counterfeit sales."

As for Amazon, it told CNBC that it's already actively dealing with bad actors on its platform, but that it will continue working with authorities on the issue: