(CNN) - Republican Rep. Peter King of New York said he doesn't want to be "reinventing" the wheel on the gun bill in the Senate and plans to make a similar background check proposal in the House with Rep. Mike Thompson, D-California.
"My goal would be to get the strongest background check bill we can," King said.
His office has been in touch with GOP Sen. Pat Toomey's office. The senator from Pennsylvania teamed up with Sen. Joe Manchin, D-West Virginia, in last-minute talks to reach a bipartisan deal that could get enough support in the Senate to pass.
The deal will expand the background check system for gun purchases to gun shows and internet sales.
A Democratic leadership source said the compromise will likely be the first amendment to gun legislation being considered.
But with Republicans in control in the House, any bill passed by the Senate is expected to face an uphill battle in the lower chamber.
House Speaker John Boehner repeated his line Wednesday that the House will "review" whatever the Senate passes and emphasized a need to better enforce the current system in place.
"We are not enforcing the laws that we have on the books today," he said at a press conference on Capitol Hill. "So if we are going to have a background check that is in the law let's make sure we do a real background check which in not all cases actually happens."
King admitted he was an "outlier" within House GOP on gun issue and said he has not talked to Boehner or other leaders yet about the bill. His counterpart, Thompson, chairs the House Democratic gun task force.
The New York congressman said Tuesday he supports universal background checks–which goes beyond the Toomey-Manchin deal–and opposed efforts by Republican senators who've vowed to block debate on the Senate bill.
"This is an issue which has grabbed hold of the American people. It is an issue, I think, an issue that has to be resolved. And even if it doesn't go down the way I want it to, I think the American people are entitled to a debate," King said on CNN's "Starting Point."
- CNN's Dana Bash contributed to this report.