WASHINGTON (Reuters) - Bank lobbyists are setting their sights on the U.S. House of Representatives, hoping the lower chamber will push the Senate to further relax regulatory oversight of larger banks, several people familiar with the situation said.

The Senate looks set in coming months to pass the first revision of rules introduced following the 2007-2009 financial crisis, after Banking Committee Chairman Mike Crapo, a Republican, secured the necessary support from Democrats to advance a bill easing up on community lenders.

The bill, which took months of bipartisan negotiations, proposes to raise the asset threshold at which banks are considered systemically risky and subject to stricter Federal Reserve oversight to $250 billion from $50 billion.

Large banks, which so far stand to gain little from the Senate bill, are making their case for further rule changes to Republican lawmakers in the House, according to the sources, who spoke anonymously, given the delicate state of negotiations.

Both chambers’ approval is needed for legislation to pass.

The House has taken an aggressive stance on rolling back the 2010 Dodd Frank Act, which advocates say provides critical protections against future financial crises. But the financial industry has been eager to rework the law, saying some of its provisions curb their ability to lend.

Republicans have tried for years to revise the law, and only recently have moderate Democrats begun to support modest changes.

Last month the House passed a bill that would scrap asset thresholds altogether, directing the Fed to focus instead on the business model of a bank when assessing its riskiness and oversight.

That bill, sponsored by Republican Blaine Luetkemeyer, drew strong support from lawmakers of both parties, buoying hopes among bank lobbyists that Senate Democrats may yet be persuaded to meet the House halfway.

One compromise some regional banks are discussing with lawmakers would keep the $250 billion threshold favored by the Senate but require the Fed to ease rules on banks it considers less risky and to treat lenders with the same business models and risk profiles equally, regardless of their size.

“Our proposal simply seeks to find middle ground between the Senate and House approaches,” said one regional bank executive. “Equal consideration should be given to the bipartisan efforts in the House.”

These changes could be a tough sell.

The Senate bill’s sponsors are willing to make minor tweaks to bring more lawmakers to the table but are wary of driving away Democrats needed to support the bill, lobbyists and congressional staff said.

It is also unclear if Republican Jeb Hensarling, Crapo’s counterpart in the House and a staunch conservative, would push for Luetkemeyer’s proposal during the negotiations.

He authored a sweeping rewrite of Dodd-Frank that passed the House in June but which the Senate largely ignored. That bill, however, did not include Luetkemeyer’s risk-based approach.

Hensarling has called the Senate bill “a good start” but is likely to push for some pieces of his Dodd-Frank rewrite to be included, according to people familiar with his thinking.

Lobbyists said they feared a too-aggressive approach by Hensarling could backfire, leading to an extreme bill that would alienate moderate senators.

But the sources close to Hensarling, who will retire at the end of 2018, said he would be willing to compromise.

Hensarling and Crapo declined to comment.