Senate Republicans are responding cautiously to a new proposal to expand background checks for gun sales that the Trump administration is circulating on Capitol Hill.

President Trump Donald John TrumpFederal prosecutor speaks out, says Barr 'has brought shame' on Justice Dept. Former Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick MORE has yet to endorse the proposal, but the White House is taking the temperature of Senate Republican support for the idea.

“There are some ideas floating around that different members of the administration are coming up with and at this point it’s probably too early to say” if Republicans will support it, said Senate Republican Whip John Thune John Randolph ThuneHouse to vote on resolution affirming peaceful transition of power Trump dumbfounds GOP with latest unforced error Senate passes resolution reaffirming commitment to peaceful transition of power MORE (S.D.).

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“Our members are going to be very — proceed with caution — very skeptical of some of the ideas that have been put out there in the past, but I think they’re willing to listen,” Thune added.

Senate Judiciary Committee Chairman Lindsey Graham Lindsey Olin GrahamLincoln Project mocks Lindsey Graham's fundraising lag with Sarah McLachlan-themed video The Hill's Morning Report - Sponsored by Facebook - Republicans lawmakers rebuke Trump on election Trump dumbfounds GOP with latest unforced error MORE (R-S.C.) said he has not yet reviewed the administration’s memo on expanding background checks, which is along the lines of the amendment sponsored in 2013 by Sens. Pat Toomey Patrick (Pat) Joseph ToomeyAppeals court rules NSA's bulk phone data collection illegal Dunford withdraws from consideration to chair coronavirus oversight panel GOP senators push for quick, partial reopening of economy MORE (R-Pa.) and Joe Manchin Joseph (Joe) ManchinThe debate over the filibuster entirely misses the point Trump plans to pick Amy Coney Barrett to replace Ginsburg on court Day before Trump refused to commit to peaceful transition, Aaron Sorkin described how he would write election night MORE (D-W.Va.).

“I haven’t seen it but I talked to [Attorney General William] Barr yesterday. He’s going around talking to people. If he’s good with it, I’m good with it,” Graham said of the memo.

The memo, titled, “Idea for New Unlicensed-Commercial-Sale Background Checks,” proposes expanding background checks to all advertised commercial sales, including sales at guns shows, along the lines of the Manchin-Toomey proposal.

The document was first reported on by The Daily Caller.

Toomey, a lead Republican negotiator on expanding background checks, told reporters Wednesday that Barr, not the White House, drafted the memo.

"I have spoken with the attorney general. I think I have a pretty good idea of what he has in mind. I think it's a very thoughtful, very constructive, very creative way to accomplish some important goals," Toomey said.

"I think a number of things are still in a work in progress, to some degree," he added.

The memo floats the idea of conducting background checks for all commercial sales either through a federally licensed firearms dealer or a newly created class of licensed transfer agents.

Licensed transfer agents would not have an inventory of guns to sell but would be authorized by the Bureau of Alcohol, Firearms and Tobacco to conduct background checks through the National Instant Criminal Background Check System (NICS).

Under the proposal, all commercial gun sales would produce two forms, a bill of sale that would record the details of the sale, and a certification from either a licensed firearms dealer or transfer agent recording that a successful background check has taken place.

If someone who attempts to buy a firearm fails a background check, that would be reported to law enforcement officials.

If the buyer passes the background check and purchases the firearm, the person who sells the gun would receive a copy of the form certifying that a successful background check was performed. Licensed gun dealers and transfer agents would not maintain these records, a provision intended to allay fears by Second Amendment advocates that the proposal could lead to the creation of a federal firearms registry.

The record-keeping requirements of the proposal would be enforced by civil penalties. People who sell guns would be granted the same civil immunity as federally licensed firearms dealers, according to the memo.

Sen. Josh Hawley Joshua (Josh) David HawleyHillicon Valley: Subpoenas for Facebook, Google and Twitter on the cards | Wray rebuffs mail-in voting conspiracies | Reps. raise mass surveillance concerns Trump faces tricky choice on Supreme Court pick FBI director warns that Chinese hackers are still targeting US COVID-19 research MORE (R-Mo.), who met with Barr to discuss the proposal, said he’s still evaluating it and wants to know what Trump will wind up supporting.

"My question to the attorney general ... was what is the president going to support? What is the president going to put forward?” Hawley told reporters.

Asked about the specifics of the memo, Hawley said, "I need to evaluate it. It's more sort of a, I don't want to say thought experiment ... but it's more in the way that here's some ideas that one could turn into a concrete proposal."

Hawley said Barr appears to be more brainstorming with GOP senators on expanded background checks instead of actively trying to sell them on the new ideas.

Sen. John Cornyn John CornynHillicon Valley: Productivity, fatigue, cybersecurity emerge as top concerns amid pandemic | Facebook critics launch alternative oversight board | Google to temporarily bar election ads after polls close Lawmakers introduce legislation to boost cybersecurity of local governments, small businesses On The Trail: Making sense of this week's polling tsunami MORE (R-Texas), a senior member of the Judiciary Committee who also has been involved in gun violence talks, said the administration’s memo is not a final offer to Capitol Hill.

“It’s not final by any means. The president hasn’t endorsed it, and there’s some question about when the president might actually do that,” he said.

Sen. Chris Murphy Christopher (Chris) Scott MurphyDemocratic senator calls for 'more flexible' medical supply chain to counter pandemics The Hill's 12:30 Report - Presented by Facebook - Don't expect a government check anytime soon GOP chairman to release interim report on Biden probe 'in about a week' MORE (D-Conn.), a leading gun control advocate who has participated in negotiations with the White House and fellow senators on expanding background checks, questioned why the proposal hasn’t been shared with Democrats.

“Not a single Democrat has seen this or signed off on it and my understanding is the president hasn’t approved it either. It’s hard to know whether this is constructive or not,” he said.

Murphy said he plans to speak to White House officials Wednesday afternoon.

Sen. Ron Johnson Ronald (Ron) Harold JohnsonThe Hill's Morning Report - Sponsored by Facebook - Trump previews SCOTUS nominee as 'totally brilliant' The Hill's 12:30 Report: Ginsburg lies in repose CHC leaders urge Senate to oppose Chad Wolf nomination MORE (R-Wis.) said White House legislative affairs director Eric Ueland presented some ideas for addressing gun violence during a meeting with GOP senators Monday night.

“There really is a very sincere and concerted effort to find areas where we can actually have effective measures passed that will help prevent, help mitigate where there are some of these mass shootings,” he said.

However, Johnson also sounded a note of skepticism.

“We all do realize that no matter what we do on guns, it’s not going to prevent these tragedies,” Johnson said. “There will always be a black market for some portion of those 400 million guns."

Asked whether he could support a proposal along the lines of Manchin-Toomey, Johnson noted, “I voted against it the last time.”

“In the end, the evaluation does come: What’s the purpose of this? Is it really going to prevent any of these [mass shootings?] No,” he said.

Ueland on Wednesday declined to say which White House officials were involved in drafting the ideas sheet.

“The president has asked us to respond and listen to perspectives, views, opinion and ideas, and tips, from members of Congress and that’s what we continue to do here,” he told reporters.