Raseriti Tau, who chairs the NCOP special committee processing the Bill, told the Mail & Guardian this week that the committee was working hard to achieve consensus to avoid political parties having to vote on the proposed legislation.
"I don't want to see the process leading to a vote. That is why we are encouraging dialogue," said Tau.
Parties have been meeting behind the scenes to "find each other" since the committee last sat on August 7.
This is a major shift from the National Assembly process, in which the ANC used its majority to outvote the opposition and pass the Bill amid protests from both inside and outside Parliament in November last year.
There have been rumours over the past week that the next meeting of the committee will be its last, which means the Bill will be pushed through without the committee having thoroughly worked on it.
"I can't see how that can be a final meeting," said Tau.
"There is still so much to be done, including discussing the desirability of the Bill, which is another process. Even after the discussions we will have to adopt the Bill clause by clause," he said.
Deliberations on the Bill will resume on August 29, but the agenda would be determined by how much progress political parties had made in their discussions, said Tau.
He said he had not been part of the talks because "I don't want to compromise my independence".
A source close to the committee said the NCOP would "surprise many" and propose further amendments to the Bill.
Tau would neither confirm nor deny this.
In May, the ANC bowed to pressure and proposed an amendment that gave increased protection to journalists and whistle-blowers. The acting director general of state security, Dennis Dlomo, caused a stir by shooting down many of the mooted amendments to the Bill.
At the time, Tau denied that the department was trying to bulldoze the committee and said the process was one of "engagement".