The Los Angeles Times said the proposal is similar to the blueprint proposed by the bipartisan group of senators on Monday. The group has been meeting regularly since the November election.
Two congressional aides talked to the Times on the condition of anonymity because the negotiations are sensitive, the newspaper said.
The aides told the Times the proposal includes a path for illegal aliens to become legal, new border security measures and tighter restrictions on employers who hire aliens.
In a statement, Rep. Mario Diaz-Balart, R-Fla., said the senators' principles "are compatible with discussions in the House," but would not give details or confirm he is in the group, the Times said.
But congressional aides told the Times Diaz-Balart, Republicans John Carter and Sam Johnson, both of Texas, are in the group, as are Democrats Luis V. Gutierrez of Illinois, Zoe Lofgren of California and Xavier Becerra of California, the chairman of the U.S. House Democratic caucus.
In his own statement, Gutierrez said he has been a part of "very constructive conversations with my House colleagues in both parties" who are "poised for action and not just more talk on immigration reform." The Times said he also would not confirm that he is part of the group.
The newspaper said the negotiations have been approved by House Speaker John A. Boehner, R-Ohio, and Minority Leader Nancy Pelosi, D-Calif. The Times said Boehner has not promised he would support the bill, but wouldn't stand in the way .