Sen. Todd Young, a Republican from Indiana, is seen as the favorite to fill the party’s open seat on the Finance Committee, according to a Senate Republican aide and a tax lobbyist familiar with discussions.

Young’s name has been thrown around consistently, especially because of the time he spent on the House Ways and Means Committee, the aide said on the condition of anonymity in order to talk freely about the discussions.

Young was a House representative for six years before his election to the Senate in November 2016. He won a seat on the Ways and Means panel—which...