The bill, presently in committee in Albany, was drafted by state senator Kevin Parker and Brooklyn Borough President Eric Adams, the Washington Times reported.
The proposed changes to background checks would allow for authorities to go back three years on social media before making a determination.
"We've obviously seen some of the mass shooters have a social media history that should have sent red flags," said Paul McQuillen, director of the Buffalo chapter of New Yorkers Against Gun Violence. "There should be more restrictions on how guns are purchased. We should have more background checks."
Gun rights attorney James Tresmond, disagreed, arguing that such a law would violate some of the most basic freedoms afforded to Americans in the Bill of Rights and beyond.
"The first, the second amendment, the fifth amendment, the fourth amendment, and the 14th amendment" would be violated, he argued, according to the Washington Times. Those amendments deal with issues of speech, the government's authority to search citizens, the right to bear arms and self-incrimination.