Just a day after Trump's stunning election victory over Democrat Hillary Clinton, congressional aides told Reuters the lawmakers wanted to meet with Trump's advisers to discuss a less costly option to his "big, beautiful, powerful wall."
The plan would involve more border fencing and additional border staffing with federal agents, many of whom belong to labor unions that supported Trump's candidacy, the aides said.
Double layers of fencing would be extended along parts of the roughly 3,200km border, rather than constructing a brick-and-mortar wall, according to the proposal.
A House Republican aide and a Department of Homeland Security official said a wall was not realistic because it would block visibility for border agents and cut through rugged terrain, as well as bodies of water and private land.
The House aide said House Republicans working on the alternative plan were waiting for Trump's transition team to be put in place before setting a date for the meeting.
A spokesperson for Trump did not respond to a request for comment on the lawmakers' proposal or their desired meeting.
Mexico said on Wednesday that it would not pay for a border wall, as Trump has pledged.
Immigration was a central feature of the Trump campaign, focusing on concerns among some voters about illegal immigrants and perceptions they take jobs and pose security risks.
Before the Republican convention in July, party platform committee members successfully petitioned delegates to add language about the proposed wall to the platform statement.
But US Republican Representative Michael McCaul, chairperson of the House Homeland Security Committee, has called a wall along the entire border a "knee-jerk" reaction and has not mentioned the idea in legislation on Capitol Hill.
If Congress stands up to Trump, his wall may end up being a fence extension, said Steve Legomsky, professor emeritus and immigration law expert at Washington University School of Law.
