ST. PAUL -- U.S. Sen. Amy Klobuchar says she has a job, which includes vetting any U.S. Supreme Court nominee, and is not seeking a position herself on the high court.

Her Senate Judiciary Committee post is important as the president and Senate work to replace Justice Antonin Scalia, who died during the weekend at 79, the Minnesota Democrat said Tuesday.

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"There are a many wonderful, qualified people who could serve on the Supreme Court, but only a few of us are charged with the job of getting the nominee through the Senate," Klobuchar added.

In a Tuesday interview with Forum News Service, Klobuchar never categorically said she would reject a Supreme Court nomination.

"I have a job and I don't want to shirk it," Klobuchar responded when asked in the interview about whether she would accept an Obama nomination to be justice.

"I love my job representing Minnesota in the Senate," she added. "Clearly, there is still a lot of work yet to be done in Washington. In this time in highly polarized politics I think the work that I am doing is important."

Talk about a potential justice nomination or a run for president or vice president has swirled around Klobuchar since early in her Senate tenure. She told Forum News Service before her 2012 re-election that she would serve out her six-year term.

MSNBC's Rachel Maddow did nothing to slow that talk when she promoted Klobuchar's Tuesday night appearance on her show.

"Maybe he (President Barack Obama) will just cut to the chase and pick an actual senator, a centrist who doesn't have any enemies in the Senate, or the world," Maddow said. "Squeaky clean. Somebody who's on the Judiciary Committee. Somebody who is a woman. Somebody who is a former prosecutor."

USA Today put Klobuchar in its top 10 list, saying: "If the Senate would be less inclined to block one of its own, the senior senator from Minnesota, 55, might be someone Obama would consider."

CNN reported that Klobuchar would be a "groundbreaking" choice as a former Hennepin County attorney who has not been a judge.

Klobuchar is pushing for the Senate to take up a justice nomination once Obama presents it. Republican leaders have said they will wait until a new president is sworn in to consider a new justice, which senators must confirm.

Another Democratic Judiciary Committee member, Sen. Al Franken of Minnesota, agrees with Klobuchar.

"With a duly elected president and 100 duly elected senators, we should now all do our jobs as outlined in the Constitution and undertake the process of finding a qualified replacement," Franken said.

As one of 20 Judiciary Committee members, Klobuchar said she has a duty of "making a case to the country, which you can uniquely do on the Judiciary Committee, that we can't leave the position vacant and it needs to be filled as soon as possible."

At first, Senate Judiciary Chairman Charles Grassley, R-Iowa, said he agreed with Senate GOP leaders who do not want to take up a justice nomination this year. But on Tuesday, he said that he may set hearings on an Obama appointee yet this year.

“I would wait until the nominee is made before I would make any decisions,” Grassley told Iowa reporters during a conference call. "In other words, take a step at a time."

Klobuchar she said she does not think Obama will turn the nomination political and pick a liberal just to fire up Democrats to vote in November, as some have suggested.

"I think it is important that he nominate someone what would be an excellent justice," Klobuchar said. "I think he will do that."