Sen. Brad Miller, D-Wake, co-chairman of the committee, said a Senate map that is more appealing to Democrats than the one the House passed last week will be presented Tuesday.
Miller said he thinks the Senate deserves a say in the new redistricting plan.
"We have (voting) buttons too," he said. "We got elected too and should have a say."
Miller predicted that the Senate map would include slight changes to the 8th and 11th districts.
He added that senators might consider the House plan if the Senate proposal has difficulty passing the House.
But Rep. Ed McMahan, R-Mecklenburg, co-chairman of the House Congressional Redistricting Committee, urged committee members to vote for the House redistricting plan as it stands.
"(The House) would ask you to please consider voting as drawn and opposing any amendments," he said.
McMahan said he is afraid that if the Senate amends the plan, the coalition in the House will unravel and create roadblocks that will extend the legislative session.
Sen. Fletcher Hartsell, R-Cabarrus, also plans to propose a new congressional redistricting plan designed by a group of elementary school students from Odell Elementary School in Cabarrus County.