A group of GOP senators is working to translate President Trump Donald John TrumpHR McMaster says president's policy to withdraw troops from Afghanistan is 'unwise' Cast of 'Parks and Rec' reunite for virtual town hall to address Wisconsin voters Biden says Trump should step down over coronavirus response MORE's immigration framework into legislation as the chamber barrels toward a floor fight with no deal in sight.

Sen. John Cornyn John CornynAirline job cuts loom in battleground states Senate Republicans signal openness to working with Biden Hillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll MORE (R-Texas) said Republican senators — led by Sen. Chuck Grassley Charles (Chuck) Ernest GrassleySenate Republicans signal openness to working with Biden Senators offer disaster tax relief bill Trump spikes political football with return of Big Ten season MORE (Iowa), the chairman of the Judiciary Committee — are working to write a bill based on the White House's proposal.

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"That's what the discussion is," Cornyn told The Hill after a meeting with Grassley and other GOP senators, including Sens. David Perdue (Ga.) and James Lankford James Paul LankfordMcConnell works to lock down GOP votes for coronavirus bill Charities scramble to plug revenue holes during pandemic Warren calls for Postal Service board members to fire DeJoy or resign MORE (Okla.), when asked if they were drafting legislation.

Cornyn didn't specifically rule out changes to the framework as the senators create the legislation, but said they aren't going to "negotiate against ourselves."

Spokespeople for Grassley didn't respond to a request for comment.

It's unclear if senators will formally introduce the legislation as a stand-alone measure and offer it during next week's immigration debate.

Lankford also confirmed that the group is drafting legislation based on Trump's outline. That framework would give citizenship to roughly 1.8 million immigrants brought into the country illegally as children in exchange for tens of billions of dollars in border wall and security funding, and sweeping changes to legal immigration.

But it's been widely panned by Democrats, as well as some GOP senators who are wary of making changes to legal immigration as part of a deal on the Deferred Action for Childhood Arrivals (DACA) program.

Lankford appeared to signal that he had talked with Democrats as the immigration proposal is being drafted.

"I've had all kinds of conversations with Democrats saying, what changes would you need," he said.

But Lankford added that both sides are digging in, rather than trying to close the gap.

Cornyn, when asked about making changes to accommodate Democrats, also suggested there has been little headway.

"They seem to have this illusion that all they need to do is deal with about half of it," he said.

It's unclear which Democrats have been involved in discussions. Sen. Joe Manchin Joseph (Joe) ManchinBiden promises Democratic senators help in battleground states Senate leaders quash talk of rank-and-file COVID-19 deal OVERNIGHT ENERGY: House Democrats tee up vote on climate-focused energy bill next week | EPA reappoints controversial leader to air quality advisory committee | Coronavirus creates delay in Pentagon research for alternative to 'forever chemicals' MORE (D-W.Va.), who is part of a bipartisan group led by Sen. Susan Collins Susan Margaret CollinsThe Hill's Campaign Report: Biden asks if public can trust vaccine from Trump ahead of Election Day | Oklahoma health officials raised red flags before Trump rally Gideon leads Collins by 12 points in Maine Senate race: poll Senate leaders quash talk of rank-and-file COVID-19 deal MORE (R-Maine), said he hasn't talked to Cornyn or Grassley about turning the administration's framework into legislation.

Senators from both parties have floated a scaled-back bill that would link a fix for DACA to a border security package.

But the White House has shot down a proposal from Sens. Christopher Coons Christopher (Chris) Andrew CoonsBiden promises Democratic senators help in battleground states Shakespeare Theatre Company goes virtual for 'Will on the Hill...or Won't They?' The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep MORE (D-Del.) and Lindsey Graham Lindsey Olin GrahamThe Hill's Campaign Report: Arizona shifts towards Biden | Biden prepares for drive-in town hall | New Biden ad targets Latino voters Senate Democrats' campaign arm announces seven-figure investment to boost Graham challenger Graham: Comey to testify about FBI's Russia probe, Mueller declined invitation MORE (R-S.C.), which did not include funding for Trump's border wall.

The stalemate comes as the Senate could turn to a fight over immigration in a matter of days.

Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellMcConnell focuses on confirming judicial nominees with COVID-19 talks stalled McConnell accuses Democrats of sowing division by 'downplaying progress' on election security Warren, Schumer introduce plan for next president to cancel ,000 in student debt MORE (R-Ky.) has promised he will start a debate if a larger deal isn't reached by Thursday. But he's given no indication about what bill he will use as the Senate's starting point.