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(CNN) — A veteran Senate Republican from Tennessee has some advice for President Donald Trump: Stay out of the next round of border security talks.

Sen. Lamar Alexander (R-Tenn.), a close adviser to Senate Majority Leader Mitch McConnell, told CNN that the involvement of both Trump and House Speaker Nancy Pelosi would complicate efforts to get a border security deal before a mid-February deadline to avert another government shutdown. And he called for any House-Senate agreement on border security to include legislation preventing shutdowns from happening in the future — an idea picking up bipartisan steam.

“We know the President’s positions. And we know Speaker Pelosi’s positions. Now, let them step back and let the conference committee do what it usually does,” Alexander said, pointing to efforts to fund physical barriers in the past.

Alexander’s comments reflect the growing unease among Senate Republicans over the prospects of another shutdown, which Trump raised Sunday as a possibility during an interview with the Wall Street Journal.

McConnell privately told Trump last Thursday that GOP senators were growing impatient over the shutdown, a source told CNN, and a number of Republicans openly expressed their frustration with the 35-day shutdown and the lack of a White House strategy to end it.

After Trump agreed Friday to reopen the government for three weeks, a 17-member House-Senate conference committee will convene Wednesday to begin talks over a homeland security spending bill that would serve as a vehicle for immigration and border security measures. Trump has demanded $5.7 billion to fulfill his campaign promise for a wall at the southern border, something that Pelosi has flatly rejected.

But Pelosi on Friday was unclear about whether she would rule out funding for the wall in the next round of talks. And some Democrats have signaled an openness to compromise in exchange for immigration policy changes, such as legal status for undocumented immigrants brought to the United States at a young age, recipients of the Deferred Action for Childhood Arrivals program. Trump told the Journal that he was not inclined to support such a deal that would pave the way for a pathway to citizenship for DACA recipients, also referred to as Dreamers.

With Trump saying that another shutdown is an “option,” Alexander called for legislation to prevent that from happening again.

Two separate measures, offered by Sens. Rob Portman of Ohio and Mark Warner of Virginia, respectively, would outline different ways to stop the threats of shutdowns if Congress and the White House fail to reach a deal to fund the government.

Alexander said a final House-Senate deal to fund the Department of Homeland Security should also incorporate provisions from those bills.

“Legislation designed to make shutdowns a relic of the past, which is where they belong, they belong in the dustbin of history — and not our future,” Alexander said. “And there’s broad support for that on both sides of the aisle. I would hope that whatever agreement we come to in the end of three weeks would include some version of Sen Warner or Sen. Portman’s bill.”

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