As the Senate’s bipartisan border negotiators sound an optimistic note about presenting a potential agreement to their colleagues next week, one of them — Arizona Independent Kyrsten Sinema — separately revealed that she spoke with Speaker Mike Johnson on Friday.

“We’ve been talking about briefing the two [Senate] conferences next week,” Sinema told reporters. “I think we are on track to do that.” She declined to offer any details about her separate conversation with Johnson.

Senators will return to Washington on Monday and will hold full party meetings on Tuesday. Sen. Chris Murphy (D-Conn.), his party’s leading negotiator, echoed Sinema’s hopes of securing at least the outlines of a deal by early next week, though he was skeptical and made clear there is no agreement yet.

“We’ve already blown through the deadlines we had established for ourselves in 2023 … I don’t know that we’ll get there,” Murphy said. “We still have a couple outstanding issues that we’re working hard at.”

Clinching even a partial agreement on stricter border policy by early next week would be the most notable sign of progress in two months of negotiations among Murphy, Sinema, Sen. James Lankford (R-Okla.) and the Biden administration. If it happens, it couldn’t come at a more high-stakes time: The first batch of government funding runs out on Jan. 19, and House conservatives are already beginning to signal interest in trying to force a shutdown if a border deal isn’t reached that’s to their liking.

Johnson’s involvement also signals that talks are progressing to the point of briefing the House, where many lawmakers worry that Republicans could quickly reject any Senate deal. Conservatives are already pushing more border restrictions than Democrats can stomach, and if Johnson embraces a Senate proposal that’s unpopular with the right, he could face a problematic rebellion with a reed-thin majority.

A Johnson spokesperson did not immediately return a request for comment about his conversation with Sinema.

Senate negotiators spent the past few weeks facing questions on whether to welcome the speaker’s engagement in their work, or whether the lack of it showed they were pursuing a flawed strategy.

“You’ve got to get a bill through both chambers to get it signed by the president,” Sinema said. “So we’re working very hard to ensure that this is a bill that can pass both the Senate, the House and get signed by the president.”

Both Sinema and Murphy declined to offer specifics on whether they’re hoping to present their colleagues a framework, a bill text, or just a broad update on where negotiations stand. Their efforts are designed to create a border package that can help shake loose President Joe Biden’s $100 billion-plus emergency national security spending request — not to have any role in the domestic funding that’s set to expire soon.

“Normally how these big bipartisan deals work out is that you have a top line compromise first, and then you work to finalize the text. I don’t yet know how, if we reach an agreement, how we present that to our colleagues,” Murphy said.

Negotiators are expected to make some changes to U.S. asylum law, including raising the credible fear standard and an expulsion authority similar to the Trump-era Title 42 policy, according to three people familiar with the talks who were granted anonymity to discuss private conversations.

Department of Homeland Security officials are drafting text for these policies, according to one of the people, who asked to remain anonymous to discuss private conversations with Hill aides and administration officials.

The people further cautioned that the impact of the policies depends on how the text is written — a level of detail that hasn’t emerged from the tight-lidded talks. DHS Secretary Alejandro Mayorkas did not attend Friday’s meeting but is a regular presence in the talks; several White House officials were in attendance on Friday.

Negotiators are still working through complicated details of other potential policy changes, such as an expansion of expedited removal of migrants. The biggest sticking point remains striking a compromise over changes to the president’s parole authority, which has so far been a red line for the White House.

Sinema would not address what’s still holding up a final accord, but she told reporters that negotiators will continue to meet remotely this weekend before session resumes on Monday.

“It’s going to be very busy,” she said of the upcoming weekend.