Washington(CNN) A group of freshman Democrats is working to convince House Speaker Nancy Pelosi to draft Rep. Justin Amash as an impeachment manager for the expected Senate trial, a source familiar with the matter told CNN on Sunday.

The group is led by Democratic Rep. Dean Phillips of Minnesota, who has been in touch with the Michigan independent, who is open to the idea, the source said. The anticipated trial has the power to elevate the careers of those chosen for the high-profile job of officially presenting House Democrats' case, so different members are angling for those jobs.

CNN reached out to Amash and Phillips on Sunday for comment. The Washington Post first reported the group's effort.

A House official close to the impeachment inquiry told CNN on Sunday that Pelosi is "highly unlikely" to name Amash as one of the impeachment managers.

"It's highly unlikely that the speaker would take this sort of risk when she has so many of her own well-qualified members clamoring for a spot," the official said.

Amash, who left the Republican Party earlier this year, told CNN earlier this month that he was prepared to vote on three articles of impeachment against President Donald Trump: obstruction of Congress, obstruction of justice and abuse of power. He cautioned though he would wait to see the final language before ultimately committing his vote.

"I think there's sufficient evidence for all three," Amash said on his way to the House floor at the time. "Impeachment is like an indictment. We're just issuing the charges. The trial happens in the Senate. There's certainly probable cause to issue charges."

The House Judiciary Committee on Friday voted to send two articles of impeachment against Trump to the House for a full vote. That vote, expected this week, will set up a trial in the Senate.

The House will consider will consider a charge that Trump abused his power by withholding nearly $400 million in US military aid and a White House meeting while pressuring Ukraine's president to investigate a potential political rival. The second charge accuses Trump of obstructing Congress by thwarting the House's investigative efforts.

Senate Judiciary Chairman Lindsey Graham on Saturday told CNN's Becky Anderson at the Doha Forum in Qatar that he would do everything in his power to make the impeachment trial "die quickly" in the Senate.

"This thing will come to the Senate, and it will die quickly, and I will do everything I can to make it die quickly," the South Carolina Republican said.

He later added: "I am trying to give a pretty clear signal I have made up my mind. I'm not trying to pretend to be a fair juror here. What I see coming, happening today is just a partisan nonsense."

Amash on Saturday joined a chorus of Democrats criticizing Graham for his remarks.

"Senator Graham has chosen to violate his oath to support and defend the Constitution, his oath to do impartial justice in an impeachment trial, and his duty to represent all the people of his state, not just those who share his political views or desire a particular outcome," Amash tweeted.