Lieberman, one of the bill’s sponsors, told Jennifer Martinez that Majority Leader Harry Reid had confirmed that timetable.
He added he is trying to get as much agreement as possible on two controversial topics of the legislation: information sharing and performance requirements.
Initially introduced in February, the bill sponsored by Lieberman, Susan Collins, Jay Rockefeller and Dianne Feinstein will put the Department of Homeland Security in charge of assessing national infrastructure.
Lieberman said that they would update the cybersecurity bill with the help of the White House to address issues on information sharing and infrastructure.
He added the new version might be enough to get 60 votes in the Senate.