President Donald Trump told CNBC on Thursday he is "willing to shift more" on his border security and DACA demands if that's what is required to reach an immigration deal that will pass Congress in February.

This includes supporting a path to citizenship for approximately 1.8 million undocumented young people who were brought to the U.S. as children and are eligible for Obama-era DACA protections against deportation, NBC News reported.

"We're going to solve the DACA problem," Trump told CNBC's "Squawk Box" in an interview from Davos, Switzerland.

Trump said he believes that a core group of congressional Republicans who have been advising him on immigration would be willing to shift their positions, too.

"I think Cotton and Perdue and Goodlatte and the people that I've been dealing with — Cornyn, so many of the people — these are great people. These are people that really have shifted a lot. ... And I think they're willing to shift more, and so am I," Trump said, referring to Rep. Bob Goodlatte of Virginia and Sens. Tom Cotton of Arkansas, David Perdue of Georgia and John Cornyn of Texas.

"These are people that have very strong opinions on DACA and on immigration generally, and I happen to think they're largely right," Trump said in the interview with CNBC's Joe Kernen. Asked whether these lawmakers would agree to back a path to citizenship for DACA-eligible young people, Trump sounded optimistic. "If we make the right deal, I think they will," he said.