Top GOP senators on Monday signaled support for Donald Trump’s plan to oust the current FBI director in favor of firebrand loyalist Kash Patel, while keeping the door open for Pete Hegseth, who faces a slate of misconduct allegations, as the president-elect’s pick to run the Pentagon.

Sen. Joni Ernst, who sits on the Armed Services Committee and is seen as a key potential swing vote, issued a positive assessment of her meeting with Hegseth on Capitol Hill on Monday.

Ernst said that her conversations with the veteran and former Fox News host have been “encouraging,” and that he has “committed to completing a full audit of the Pentagon and selecting a senior official who will uphold the roles and value of our servicemen and women — based on quality and standards, not quotas — and who will prioritize and strengthen my work to prevent sexual assault within the ranks.”

The statement shows that Hegseth has made progress in his attempt to win over senators after his nomination appeared to be in serious jeopardy last week over a 2017 sexual assault allegation as even Trump allies in Congress expressed concerns.

Trump has continued to back Hegseth, however, setting up a challenge for any GOP senator who might go up against the pick. It is still early in the vetting process for Trump’s Cabinet nominees and confirmation votes won’t take place until next year. But it is clear that GOP senators are being careful to pick their battles and cautious of how they approach the president-elect’s selections.

Hegseth denies any wrongdoing and has forcefully pushed back against the allegations against him, describing them as unfounded attacks. He told CNN on Monday that he had a “very good meeting” with Ernst.

Still, when pressed by CNN, Ernst would not say whether she feels confident with Hegseth’s denials over the allegation. “I’ll refer you back to the statement,” she said. Ernst added, “It’s to be determined” if she will have another meeting with Hegseth.

Ernst also said that she spoke with Hegseth about his feelings on keeping women in their current roles in the military. “He is very supportive of women in the military. It is one thing that we discussed,” she said. Hegseth has previously said that women should not serve in combat roles.

And so far, Senate Republicans appear to be falling in line behind Trump’s pick for Patel to run the FBI.

Putting Patel in charge of the FBI would require forcing out Director Christopher Wray, who was appointed by Trump, before his term expires, and would put a self-described enemy of the so-called deep state at the head of the nation’s top law enforcement agency.

Sen. John Cornyn of Texas said Monday that he is inclined to support Patel to be FBI director, while Ernst said Trump’s pick will “create much-needed transparency” at the agency after meeting with Patel on Capitol Hill.

Sen. Chuck Grassley of Iowa, the incoming chairman of the Senate Judiciary Committee, sent a scathing letter to Wray and his top deputy on Monday, saying he has “no confidence” in the current leadership of the bureau.

Later, Grassley indicated that Patel agreed with him on his criticism of the FBI and its current director.

“He wants to make sure that congressional oversight works,” Grassley said of Patel.

Cornyn said he did not know what Wray’s plans were, but he expects Patel to be confirmed.

“I assume that Mr. Patel will be confirmed as the next FBI director. We talked about the importance of restoring the reputation of the FBI as a nonpartisan law enforcement investigative agency,” the Texas Republican said.

Cornyn said after their conversation that he is “certainly inclined to support him – barring some unforeseen circumstances.”

Asked whether he believes Wray should resign or wait to be fired, Cornyn said, “I’m not going to get involved in that. That’s up to President Trump and Director Wray.”

Asked about Patel’s history of controversial comments, Cornyn said, “I interpret that as hyperbole and I think he will tell you that same thing.”

Patel has heavily criticized the FBI and, in a podcast interview in September, called for the agency’s headquarters in Washington, DC, to be dismantled and turned into a “museum of the deep state.”

Separately, Sen. Lindsey Graham indicated that he is open to supporting Tulsi Gabbard’s confirmation as director of national intelligence, despite their disagreements on key policy issues, including US support for Ukraine. His comments came after he met with Gabbard on Monday.

“We’ve had policy differences … but you know, she’ll be serving Trump. We’ll see how the hearing goes. I like her,” the South Carolina Republican said.

On Trump’s pick to lead the Pentagon, Graham said he still has concerns but that Hegseth was “candid and he gave explanations to my concerns.”

Graham said he is “predisposed to support nominees” and “we’ll see where it goes.”

This story has been updated with additional developments.

CNN’s Ted Barrett, Morgan Rimmer, Aileen Graef and Ali Main contributed to this report.