A summary being circulated alongside the amendment called the narrowing of allowed uses of shared cyberthreat information a "very significant privacy change."
The manager's amendment was first reported by The Hill.
But the changes are not yet enough to move Sen. Ron Wyden, one of the CISA's most fervent opponents in the Senate.
"I appreciate that the sponsors of this bill have begun working on a manager's amendment to address some of the very serious concerns that have been raised, but I would say to my colleagues that this bill needs a lot more work," the Oregon Democrat said on the Senate floor after Majority Leader Mitch McConnell moved to open debate on CISA.
"The manager's amendment does not fix the provision of this bill that will allow private companies to hand large volumes of their customers' personal information over to the government with only a cursory review, even if that information is not necessary for cybersecurity," Wyden continued.
A coalition of privacy groups have been mounting a coordinated advocacy push against the bill this week, generating more than 6 million faxes from Americans urging lawmakers to vote against it.
Drew Mitnick, policy counsel at Access, said Monday that the changes in the proposed amendment do not address the privacy group's surveillance concerns. "The changes under the manager's amendment would not stop the government from instantly passing along information to intelligence agencies or keep law enforcement from using information to prosecute whistleblowers," he said.
While the manager's amendment is a first step toward making the changes to CISA that senators want to see, it is separate from a deal that would green-light a bundle of Republican and Democratic amendments in exchange for speedy consideration of the bill.
Sen. Chuck Schumer, who said last week that a deal was in the works, reiterated to reporters Monday the need for amendments on CISA.
"We want to get to the bill. It's only fair to get a few amendments," the New York Democrat said. "Republican leadership has always said that they don't want to fill trees and they want to allow amendments. We have some members who feel strongly about certain amendments, and they should be allowed to offer them."
Asked about progress toward a deal, a spokesman for Schumer said Monday it did not yet exist. McConnell spokesman Don Stewart said senators are "still working on it."
"There is no agreement on amendments," a Senate Democratic aide said Monday. "If Sen. McConnell doesn't seek [unanimous consent], the timeline on votes takes us into Friday, so not sure what he's planning here."
Sen. Rand Paul, another outspoken privacy advocate, told National Journal on Monday that he would not vote for CISA in its current form. He called for amendments, including one that he put forward.