WASHINGTON — Senate negotiations to impose tougher immigration and asylum laws have moved to a new phase as the group is now working with key senators to finalize the funding provisions in the deal, three sources familiar with the talks said.

The immigration group is working with the Senate Appropriations Committee on how to craft the funding language to match the policy changes the negotiators have largely agreed to.

There are varying levels of optimism among senators and aides that the development could mean the group has locked in an agreement. But shifting the conversation to appropriators demonstrates that negotiators have made progress toward an agreement on border provisions.

“We’re at the point of drafting and finalizing text. We don’t have an enormous amount of work left to do,” Sen. Chris Murphy of Connecticut, the chief Democratic negotiator, said Monday afternoon.

He added that “it’s possible” the Senate would start voting on the bill this week. “You can’t just change policy,” Murphy said. “You’ve also got to fund the policy.”

A source familiar with negotiations said the major policy sticking points are largely resolved, but another source noted that nothing is agreed to until the full package is finalized.

The lead negotiators — Murphy and Sens. Kyrsten Sinema, I-Ariz., and James Lankford, R-Okla. — met virtually Monday morning before the Senate returned to Washington, a source said.

“It will be, by far, the most conservative border security bill in four decades,” Lankford told NBC News.

Sen. Dick Durbin, D-Ill., who chairs the Judiciary Committee, which oversees immigration, said he doesn’t expect the emerging deal to go through committee, which would have slowed the process.

“It goes directly to the floor,” he said, adding that he expects senators will have “a day or two” to read it over and that the Senate can pass it “in a week” once an agreement is finalized.

Durbin said it’s “a good sign” that appropriators are reviewing the emerging pact, though he said he also still needs to see the details.

“I want to see the policy,” he said.

The immigration provisions, demanded by Republicans, are poised to be attached to a national security supplemental bill that includes new U.S. aid for Ukraine, Israel and Taiwan. The package, which is expected to exceed $100 billion, will be separate from a broader government funding bill, which is being crafted on a separate track, ahead of new shutdown deadlines in early March.

The appropriators have a significant role in finalizing the immigration deal, because the policy changes under discussion will need to be adequately funded to be implemented properly. A source said the process of crafting funding bills can be complicated and require further finessing of policy details, particularly on thorny issues like curtailing the president’s power to use “parole” to admit asylum-seekers.

“We’ve come a very long way since talks began two months ago,” Senate Majority Leader Chuck Schumer, D-N.Y., said Monday. “All of us on the Democratic side are serious about getting something done.”

“We remain hopeful, but it’s certainly not a done deal yet,” he said. “There are a handful of issues that have not yet been agreed to.”

Senate Minority Leader Mitch McConnell, R-Ky., said Monday the group was working to “finalize the most substantial border security policy in 30 years,” adding: “This agreement would come not a moment too soon.”

As the Senate left Thursday, Lankford said the release of text this week was his “target” and sounded confident that negotiators would resolve the parties’ differences over parole, which had dragged out talks. He declined to reveal details but cautioned members against criticizing the deal before it is done.

“Wait till you see the bill,” he said. “People want to be able to see it. They have fair criticism. They’re getting all these rumors and things that are false. They just want to see the text.”

President Joe Biden, who would need to sign any deal into law, expressed willingness Friday to agree to “significant policy changes at the border.”

“I think next week we’re going to be able to work out something, at least in the Senate, and I’m hopeful it’s going to be a bipartisan package the Senate is going to pass, God willing,” he said. “I’m ready to solve the problem. I really am. Massive changes, and I mean it sincerely.”