Washington (CNN) Republican Rep. Liz Cheney, the daughter of former Vice President Dick Cheney and a freshman lawmaker from Wyoming, is running for the role of Republican Conference chair in House GOP leadership, a source close to Cheney confirmed to CNN.

If Cheney wins, it would make her a rising star in the Republican Party and the run for leadership puts the first-term lawmaker on a path to gain more prominence on Capitol Hill. GOP leadership encouraged her to run for the position, a Republican source with knowledge told CNN.

Cheney has been all over the country fundraising for Republican candidates ahead of Election Day and has been an active fundraiser for members of her party since she came into office. The 2018 midterm elections, where House Republicans are at risk of losing their majority in Congress, take place next week.

US Rep. Liz Cheney of Wyoming speaks during a news conference in February on Capitol Hill in Washington, DC. (Photo by Alex Wong/Getty Images)

Cheney will be out fundraising on Thursday and Friday with House Majority Whip Steve Scalise, a top Republican leader, in an effort to bolster eight different congressional races. Cheney will return to her home state of Wyoming for Election Day.

If the GOP holds the House in next week's elections and Cheney becomes House GOP Conference chair that would make her No. 4 in House Republican leadership. The position is considered critical for party communications and media strategy. If Republicans lose the House, the GOP conference chair would be No. 3 in Republican leadership, as Democrats would take over the speakership.

Read More