Sen.-elect Mitt Romney, R-Utah, leaves a meeting with other new GOP Senators and Senate Majority Leader Mitch McConnell in the Capitol on Tuesday, Nov. 13, 2018.

A spokesman for Senate Majority Leader Mitch McConnell referred questions to Romney's team. Representatives for Romney did not return multiple requests for comment.

A Republican member is departing each of the committees. Sen. Orrin Hatch, the chairman of the Finance Committee is retiring and is being replaced in the full Senate by Romney. Tennessee Republican Sen. Bob Corker, chairman of the Foreign Relations Committee, is also retiring. Sen. Dean Heller, R-Nev., is a member of the Commerce Committee, but he lost his re-election bid to Democrat Jacky Rosen.

According to two people with knowledge of the matter, Romney has told friends that he's planning to submit requests to join at least three high-profile Senate panels: the Finance Committee, the Commerce Committee, and Senate Foreign Relations Committee.

Mitt Romney, the 2012 Republican presidential nominee who was elected to represent Utah in the Senate last week, is already looking to move up the GOP leadership ranks in the chamber, CNBC has learned.

Before every Congress officially begins, lawmakers have a chance to ask for specific committee assignments. Freshman lawmakers, such as Romney, usually are last in line and don't always get what they want. However, people around Romney, who spoke on the condition of anonymity, said the connections he has made to GOP leaders throughout the last decade could help him as he looks to join the committees.

Romney became one of the faces of the Republican Party during his two attempts at running for president. He lost to Sen. John McCain in the 2008 GOP primary, but won the nomination in 2012, only to fall to President Barack Obama. Romney also previously served as governor of Democratic-leaning Massachusetts, where he signed into law a health insurance measure that set the standard for the federal Obamacare health reform law.

If Romney does pick up a committee chair, he would follow in the footsteps of fellow Utah Republican Sen. Mike Lee, who made his way onto the Senate Judiciary and Foreign Relations panels as a freshman.

Romney is known to be an occasional critic of President Donald Trump. In July, he called out the president after he appeared to side with Russian leader Vladimir Putin over U.S. intelligence agencies on the matter of Russian attacks on the 2016 U.S. election.

"President Trump's decision to side with Putin over American intelligence agencies is disgraceful and detrimental to our Democratic principles," Romney said at the time.

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Following the 2016 election, however, Trump considered Romney to be his secretary of State but later chose Exxon Mobil executive Rex Tillerson instead. Tillerson had a rocky tenure in the administration and was ultimately fired. Mike Pompeo now serves as the nation's top diplomat.

Beyond working the halls of Capitol Hill as he seeks committee seats, Romney is expected to hit the Washington social scene on Wednesday and attend a party honoring Hatch at the Ritz Carlton, according to one of Romney's associates, who declined to be named. Party leaders, senators and lobbyists are celebrating Hatch's four-decade tenure in the Senate. There will also be an announcement at the event of a library being named after Hatch at the University of Utah.

Lee is planning to attend the gathering, his spokesman told CNBC. Sen. Jeff Flake, R-Ariz., is also expected to attend the festivities, according to a person familiar with the matter.

Flake's spokeswoman, Elizabeth Jones, said he is going to be attending a reception for Hatch but did not elaborate if that was at the Ritz.

"He'll just be at the reception – he's one of the keynote speakers at the RTCA [Radio & Television Correspondents Association] dinner and will need to head over there," she said in an email.

A spokeswoman for the Orrin Hatch Foundation later confirmed Wednesday's gala.

"The Orrin G. Hatch Foundation is hosting a gala to celebrate Senator Hatch and his service in the United States. This will be a private event," the representative said.